International Training Workshop

Design and Evaluation of PressurizedIrrigation Systems

March 3-7, 2009

Sponsored by

Islamic Development Bank

Prof. Dr. Muhammad LatifDirector

Centre of Excellence in Water Resources EngineeringUniversity of Engineering and Technology

Lahore - Pakistanwww.cewre.edu.pk

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Unit ISPRINKLER IRRIGATION SYSTEM AND ITS TYPES

INTRODUCTIONSprinkler and trickle irrigations together represent the broad class of 'pressurized'

irrigation methods. In these systems water is conveyed through a network of pipes to a point in

the field where water is applied. The basic difference between surface irrigation and pressurized

irrigation is that in surface irrigation methods, soil surface of upper parts of the field is used to

transport water to lower parts of the field. Thus, surface irrigation methods are much more

affected by soil topography, infiltration and soil type as compared to the pressurized irrigation

method. Basic concepts about sprinkle irrigation and its type are discussed in this lecture.

Water is applied in droplets like rain by a sprinkler system. This method has been

developed since the early part of 20th century primarily from irrigation of lawns, orchards and

nurseries. Reduction in cost due to improvement in technology and development of light weight

aluminum pipe led its extensive use in irrigation of field crops and vegetables.

A pump is normally used to lift water from the source and pressurize it to throw into the

air for distribution by sprinklers. Other components of a sprinkle system include main pipeline,

sub-mains, laterals, valves and sprinkler heads which distribute water across the surface of the

field. A typical layout of a sprinkler system is shown in Fig. 1.1 whereas Fig. 1.2 shows different

components of a trickle irrigation system. Sprinkle irrigation has some advantages over surface

irrigation such as:

i. Sprinkler irrigation can be used on such undulating lands which are difficult or impossible

to irrigate by surface methods.

ii. Sprinkler irrigation is suitable for light and frequent watering whenever needed, such as for

germination and frost protection.

iii. Sprinkler irrigation may potentially provide better uniformity of application and high

application efficiency.

iv. More effective use of a small, continuous stream of water such as from springs or dug

wells.

Prof. Dr. Muhammad Latif, Director, Centre of Excellence in Water Resources Engineering,

Lahore

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Figure 1.1 Primary components of a typical sprinkle irrigation system.

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Figure 1.2 Components of a drip irrigation system.

Irrigation of steep and rolling topography is possible by sprinkling without producing runoff or

erosion.

v. Normally sprinkle irrigation is more efficient than surface irrigation which will result in

water saving and thus more land can be irrigated with the same water supply.

vi. Much less labour is required in sprinkle method as compared to surface methods

particularly with centre-pivot sprinkler system.

The sprinkle method has also some disadvantages which are mainly related to high cost, water

quality, climatic and environmental constraints. To off-set the cost, high value crops, vegetables

and young orchards are frequently irrigated by sprinkling. If it is unavoidable to use salty water

by sprinkling, crop damage may be reduced if good quality water is applied at the end of

irrigation to wash any salt deposited on the leaves. The use of sprinkler irrigation is less

favorable under extremely dry and windy conditions due to increased evaporative water losses

and poor distribution pattern. The efficiency may generally be improved by sprinkling during

nights and less windy periods.

TYPES OF SPRINKLE IRRIGATION SYSTEMSThere are many types of sprinkle systems and several versions of each type. Sprinkle

irrigation systems may be divided into two main groups: 1) set systems that operate when the

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sprinklers are set at a particular position in the field, and 2) the continuous move systems that

operate while the system is moving in the field based on portability, systems may be further

classified as portable, semi-portable, semi-permanent and permanent systems. Centre-pivot

system and linear move system are examples of continuous moving system.

Portable SystemA portable system has portable main lines, sub-mains, laterals and a portable pumping

plant. The entire system is designed to be moved from field to field or to different sites in the

same field. This system may be moved manually or by mechanical power. In manually moved

system called 'hand move system', the pipes are moved manually. This system has low initial

cost but labour cost is high. In the mechanically moved system, the lateral is mounted on wheels

and is moved as a unit instead of one pipe at a time. This system has high initial cost but labour

requirement is less.

Semi-Portable SystemThis system is similar to a fully portable system except that the location of water source

and pumping plant are fixed. Such a system may be used on more than one field where there is

an extended main line, but may not be used on more than one farm unless there are additional

pumping plants (see Fig. 1.3).

Figure1.3: Sprinkler with Portable Stand.

Semi-Permanent SystemA semi-permanent system has permanent mains and sub-mains which are usually burried

with risers at suitable locations for connecting the laterals, which are portable. Water source andpumping plants are stationary.

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Permanent SystemA fully permanent system commonly named as solid-set sprinkler system consists of

permanently laid mains, sub-mains, laterals, stationary water source and pumping plant. Mains,sub-mains and laterals are usually burried. Sprinklers are permanently installed on each riser.Such systems are costly and are suited to automation. This type of system is usually installed inorchards, Golf courses and nurseries.

SET-MOVE SYSTEMSSet-move sprinkle systems are periodically moved from one position (irrigation) to

another by hand or mechanically. These systems remain stationary as water is applied where theyare set. When the desired amount of water has been applied, water is turned off: the pipes aredrained and the system is moved to the next position. When the move is completed, water isturned on and irrigation is resumed at the next position. This process is repeated until the entirefield has been irrigated. Common types of set-move systems include hand-move, tow-move,side-roll and gun-type.

Hand-move systemsComponents of the system are moved by uncoupling the pipes to the next position by

manual labour. This system became popular after the development of light weight aluminumpipes. Most hand-move laterals are 50 to 150 mm (2 to 6 in) in diameter. Length of pipe sectionsmay be either 6, 9 or 12 m (20, 30 or 40 ft). These systems are least expensive but have highlabour requirement. An example of hand-move system is shown in Fig. 1.4.

Figure 1.4: Schematic View of Hand-Move Sprinkler Irrigation System.

Tow-move systemThe long lateral of the tow-move sprinkle is mounted on wheels or skids so that the

system can be mechanically pulled to the next position. A tractor is normally used to pull the

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lateral after draining water. This system is the least expensive mechanically move system. Tow-

move systems are not used extensively because moving the lateral is tedious and also damage

crop. This system has been generally used for forage and row crops.

Side-roll systemThis system is very popular type of mechanically moved system. Sections of long lateral

pipes are supported on wheels with the lateral serving as axle of the wheels (see Fig. 1.5). Length

of the lateral may be as long as 800 m (about one half of a mile) and diameter is normally 100 to

125 mm (4 to 5 in). A gasoline engine is usually fixed in the center of the lateral to drive it to the

next position. Common wheel diameters used for side-roll systems vary from 1.2 to 1.9 m. The

wheel diameter must be large enough to allow the lateral to pass over the crop without damaging

it. Water is supplied either in the middle of the lateral or at the end of the system. The friction

losses within the lateral pipe are reduced when water is supplied at the center of the lateral.

Figure 1.5: A Side-Roll Sprinkler System.

Gun and Boom SprinklersGun or giant sprinklers have 16 mm (5/8 in) or larger nozzles attached to long discharge

pipes. Boom sprinklers have 18 to 36 m long rotating arms and water is applied through nozzles

on the arms (See Figures 1.6 and 1.7). The anns, or booms are supported by a cable suspension

system mounted on a four-wheel trailer. Boom sprinklers apply more uniform water in smaller

droplets than gun sprinklers. But gun sprinklers are simpler to operate than booms and also less

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expensive for the farmer. Discharge of gun and boom sprinklers vary from 65 to 78 l/s (l00 gpm

to 1250 gpm) operated at high pressures ranging from 480 to 896 kPa (70 to 130 psi). Wetting

diameter may be as large as 180 m.

Raingun Sprinklers

A typical stationary or traveling raingun sprinkler system consists of a pumping plant, flexible

hose, traveler assembly and gun sprinkler (see Figure 1.7). A stationary or fix gun irrigates at one

setting which is shifted to the next field. Whereas the traveling gun is mounted on a cart and it

moves continuously across the field while applying water. The assembly is pulled either by the

flexible pipe itself or by an anchor cable stretched across the field. The unit is moved to the next

irrigation position after irrigation is completed at the first setting. Both full and part-circle

sprinklers of large size can be used equally but the part-circle sprinklers are preferred as the cart

moves in relatively dry soil. The gun sprinklers have trajectory angles ranging between 18 to 32

degrees but for average conditions, trajectories between 23 to 25 degrees give satisfactory

results. The traveling system can be used on all field sizes and shapes. These systems can be

easily transported from field to field.

Gun and boom sprinklers can be used for most crops, but their application rates are high

and large sized water drops may compact the soil surface and cause surface runoff. Therefore,

these sprinklers are more suitable for coarse-textured soils.

Figure 1.6: A Gun Sprinkler with Rocker Arm.

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Figure 1.7: Hose-Fed Traveling-Gun Sprinkler.

CONTINUOUS MOVE SYSTEMSLaterals and sprinklers of the continuous move systems are constantly moving when

applying water. These systems have become more common due to low labour cost. Main types

of continuous moving sprinkler systems are center-pivot (CP), traveler and linear-move systems.

Center-pivot irrigation systemsThe center-pivot sprinkler irrigation systems are the most popular sprinkle systems used

in many countries as shown in Fig. 1.8. A center-pivot system consists of a pipeline supported on

towers usually spaced about 61 m apart. The length of the lateral pipeline varies from

approximately 200 to 800 m but 400 m is the most common length. A center-pivot system of 400

m long lateral covers an area of 65 ha (160 acres). Water is introduced at the pivot and flows

outward through the pipeline, supplying to each of the individual sprinkler heads. Some of the

main advantages of center-pivot sprinklers are (Keller and Bliesner, 1990, p. 307)

i. Water delivery is simplified through the use of a stationary pivot point.

ii. Guidance and alignment are controlled at a fixed pivot point.

iii. Relatively high water application uniformities are easily achieved under the continuously

moving sprinklers.

iv. After completing irrigation cycle, the system is at the starting point for the next irrigation.

v. Achieving good irrigation management is simplified because accurate and timely

application of water is made easy.

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vi. More accurate and timely applications of fertilizer and other chemicals are possible by

applying them through the irrigation water which is also possible with other sprinkler

systems as well.

vii. Flexibility of operation makes it feasible to develop electric-load-management schemes.

Figure 1.8: A Center-Pivot Irrigation System

Because this system irrigates a circular area, only about 79 percent of the area of a square

field is effectively irrigated by the basic unit (Figure 1.9). With an end-gun modification, an

additional five percent of the total area can be irrigated, leaving 16 percent of the area un-

irrigated. Not irrigating 16 percent of the area increases the cost per unit area of the irrigated

land. This problem can be overcome, to a large extent, by the addition of a 'corner-pivot' system

to the conventional center-pivot machine as shown in the above figure. The corner-pivot

assembly pivots about the outer tower and applies water at the corners of the field. This increases

the irrigated area to approximately 96 percent and reduces the investment per unit irrigated area

appreciably (Callies 1978). The corner-pivot unit is folded with the last tower of the main system

when not in use.

Center-pivot systems vary a great deal in their design. Some systems use only one type of

sprinkler head and vary the spacings between the sprinkler heads on the lateral to obtain

desirable application patterns, while others use constant spacings and vary the size of the

nozzles. Combining the two principles results in other designs, in which both the spacings

between the sprinkler heads and size of the nozzles are varied. As the perimeter of a circle is

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proportional to the radial distance and the sprinkler heads at different distances from the pivot

point travel at different speeds, the time during which water is applied to a point is also different

along the lateral. To compensate for this and to achieve reasonably uniform depth of water, the

application rate is low near the pivot and increases toward the end tower. Such a distribution of

application rates may cause undesirable runoff near the end of the system on soils of low water

intake rate.

Figure 1.9 Area irrigated by the main system, corner-pivot assembly and endgun of a center-pivot system (only one-fourth of field is shown).

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Linear Move SystemsLinear-move systems have been developed in response to the problems of irrigating the

corners and runoff associated with the center-pivot system. Linear move systems have towerswith electric motors and alignment systems, just as do center-pivot systems. The lateral movescontinuously in a linear fashion across the field rather than rotating about a central pivot point.Water is supplied to the lateral through a flexible hose hooked to a mainline or by a travelingpumping plant that pumps water from an open ditch. Recently, a linear-move system that movescontinuously and obtains water from risers connected to a buried mainline by automaticallyconnecting and disconnecting itself from riser valves has been developed.

Linear moving systems may travel forth and back, i.e. they travel twice the length of thefield to complete each irrigation cycle. Hence, the sprinklers may operate continuously forth orback, or for only half of the total distance traveled on both sides. Each method has its ownadvantages and disadvantages.

If the sprinklers are operated continuously, the total operating time will be longer. Thiswill reduce system flow and application rate requirements. However, the area that is mostrecently watered near the end of the field will be immediately re-watered each time on the moveof lateral in reverse direction. On the other hand, if the system is returned with the water shut off(or empty) the operating time will be decreased accordingly.

The continuous versus part-time watering and the possibility for backtracking overrelatively dry rather than fully irrigated soil leads to following irrigation strategies.1. Irrigate in only one direction and return empty (with the water off) as quickly as possible

to the starting point.2. Irrigate while traveling at the same speed in both directions,3. Irrigate half the field and quickly continue to the other end with the water off, then on the

return irrigate the other half of the field and quickly continue back to the starting pointwith the water off, and

4. Proceed as in strategy 3 but continue as quickly as possible with the water on (instead ofoff) during the last half of travel in either direction.

The purpose of strategy 3 is to eliminate returning across soil that has just been fullyirrigated. Otherwise it is like strategy 1. The purpose of strategy 4 is to reduce the hazardassociated with watering back across the area at the end that has just been fully irrigated.However, both strategies 3 and 4 require more management and labour than 1 and 2.

COMPONENTS OF A SPRINKLE IRRIGATION SYSTEMPrimary components of all sprinkle systems are similar in many respects. They consist of

sprinkler with or without risers, laterals, main pipeline and pumping plant as shown in Fig. 1.1.Different types of valves and couplings also form integral parts of any system. More detail of theabove components is discussed next.

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Types of SprinklersThe sprinklers also called sprinkler heads form an important component of any sprinkle

system. Water is sprayed like raindrops through these sprinklers. There are many types of

sprinklers available to suit different farming and climatic conditions. The sprinklers may be

either rotating or fixed type. Rotating sprinklers have three types: impact, reaction and gear-

driven sprinklers. Fixed-head sprinklers include spray-type and perforated pipes.

a) Rotating Head Sprinklersi) Impact Sprinklers: Impact sprinklers have one or more nozzles that discharge jets of

water into the air. These jets are rotated in a start and stop manner by a spring loaded arm which

strikes (impacts) and then is bounced out of one of the jets. The spring returns the arm to strike

the jet again and the process is repeated. Several different nozzle types have been developed for

impact sprinklers including constant-diameter, constant discharge, and diffuse-jet nozzles.

Constant-diameter nozzles are the most commonly used with impact sprinklers. The discharge

from these nozzles is proportional to the square root of the operating pressure. Small single

nozzle sprinklers are designed at low pressures, while large multiple-nozzles require high

operating pressure. Usually, low cover larger areas and also have high application rates per

nozzle.

Constant-discharge nozzles are also used with impact sprinklers. These nozzle pressures

are associated with a small diameter nozzle, small wetted area and low water application rates.

On the other hand, large size nozzles require high operating pressures, are constructed so that as

long as the operating pressure exceeds a threshold value, changes in pressure do not affect

sprinkler discharge significantly. For example, constant discharge nozzles can be used to

minimize the variation in sprinkler discharge along laterals with fluctuating pressure caused by

undulating terrains.

Diffuse-jet nozzles are designed so that droplets are formed at a lower pressure than with

other impact nozzles. This is accomplished by using noncircular-shaped nozzle openings or

turbulence inducer at the orifice to spread (diffuse) the jet as it leaves the nozzle. Diffuse-nozzles

do not wet as large an area as do constant-diameter and constant discharge nozzles.

ii) Gear-Driven Sprinklers: Some rotating sprinklers are driven by a small water

turbine located in the base of the head sprinkler. These sprinklers are called gear-driven

sprinklers because the high rotational speed of the turbine is reduced through a series of gears.

Like impact sprinklers, gear-driven sprinklers have one or more jets that rotate around the

vertical axis of the sprinkler. Unlike the start and stop rotation of impact sprinklers, gear-driven

sprinklers rotate smoothly without the splash that occurs each time the arm of an impact

sprinkler strikes the jet.

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iii) Reaction Drive Sprinklers: Small reaction drive sprinklers are normally rotated by the

torque produced by the reaction of water leaving the sprinkler. These sprinklers usually do not

wet as large an area as do impact or gear-driven sprinklers and usually operate at much lower

pressures (70 to 210 kPa or 10 to 30 psi). Some pertinent data about different sprinklers is

presented in Table 8.1 (Keller and Bliesner, 1990).

b) Fixed-Head SprinklersFixed-head sprinklers depend on smooth and grooved cones, deflector plates, and slots to

produce full-or nearly full-circle sprays or several small holes that spray around the

circumference of the sprinkler. An example of a fixed-head spray-type sprinkler is a multi

streamlet-type fixed-head sprinkler. Many fixed-nozzle sprinklers that produce small droplets

and that operate at low pressures are currently available for center-pivot and linear-move

sprinkle systems.

RisersRiser pipe connects the rotating or fixed sprinkler head to the lateral pipe. It may be a

fixed length of pipe depending upon the height of crop to be irrigated, or it may be collapsible

pipe. Pipes from 10 to 75 mm in diameter are usually used. A minimum length of about 75 mm

on small sprinklers and 1 m on large sprinklers generally provide the best flow pattern through

the sprinkler nozzle. For over-crop sprinkling in orchards or other tall crops, the riser length may

extend from 4 to 5m. Where high risers are used, quick-couplings are often provided to enable

uncoupling during the moving of the lateral. A tripod is sometimes used to keep the uncoupled

riser in upright position.

LateralsThe lateral allows transport of water from the main pipeline or from a sub-main to the

sprinklers through the risers. The lateral pipes usually available in portable lengths of 5, 6 or 12

m are regularly spaced on the mains or sub-mains. Buried permanent laterals are however, used

for orchards, tree nurseries, and for other special sites. Quick-coupled aluminum pipe is best for

most portable laterals. A rubber gasket in the female portion of these couplings has a U-shape.

The water pressure forces the outside of the 'U' to form a water tight seal. When the water is

turned off, the seal is broken and water drains from the pipe, making it easier to uncouple and

move the lateral line to next irrigation position.

Mains and Sub-mainsMain pipelines and sub-mains convey water from the pumping unit to the laterals. In

small systems, laterals may be directly connected to the main line without any sub-mains. Main

lines may be portable or permanent. Permanent mains are used where crops require full season

irrigation. Asbesttos-Cement (Ae), polyvinyl chloride plastic (PVC) and wrapped steel pipes are

used for buried pipelines. Although aluminum is generally used for portable systems, when

wrapped it is also used for buried pipelines. Portable mains are more economical when a sprinkle

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system is to be used on a number of fields. Steel pipes are used for most permanent main lines

and for center-pivot laterals.

With water being supplied by the pipelines at desired pressures to each lateral and

sprinkler, the pipes must be strong enough to withstand expected operating and surge pressures

in case of water hammering. Buried pipes must resist overburden and dynamic surface loads,

while portable pipes must be tight and durable. PVC pipes are resistant to rust and corrosion

while steel pipes are immune to both of these. Exposure to saline or acid conditions can corrode

aluminum pipes.

Economical pipe selection: The selection of pipeline diameter is critical to the cost of

any sprinkler system. Pipeline cost consists of annual fixed cost of pipes (main, sub-mains and

laterals) and the annual operating cost of pumping water through them. The total cost further

depends on annual operation hours, costs of fuel, anticipated life and friction characteristics of

pipe material and annual interest rate. Head loss due to the friction is a function of pipe diameter.

If a small diameter pipe is used, operating cost will be more due to more friction loss but fixed

cost will be low. As the pipe diameter is increased, the operating cost will decrease but the fixed

cost will increase. The optimum pipe size is the one that minimizes the sum of the fixed- and

operating costs as shown in Fig. 1.10.

Figure 1.10 Relationship between pipe diameter, capital, operating and total costs.

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PumpsA pump is required for any sprinkle system. Centrifugal or deep-well turbine pumps are

commonly used. A pump may be stationary or it may be mounted on a movable assembly.

Pumps may be powered by electric motors or internal combustion engines using diesel, gasoline

or natural gas.

Valves and AccessoriesDifferent types of valves, joints, couplings, pressure regulators and pressure gauges are used in a

properly designed sprinkle system. Main types of valves include pressure relief valves, check

valves, foot valves, drain valves, Tee and Y valves, etc. Pressure relief valves are used to relieve

excessive pressure surges. Check valves are used on the discharge side of the pump so that if the

pump is shut off it should maintain water in the pipeline above the pump. Foot-valve on the

bottom of the suction pipe maintains water in the pump when it is not in operation and thus keep

the pump in primed condition.

PERTINENT DATA OF SPRINKLER IRRIGATION SYSTEM

Tables 1 and 2 shows water saving by using sprinkler as compared to surface irrigation

method in Pakistan and India respectively. It is apparent from these tables that more than 50%

water may be saved by using sprinkler as compared to surface irrigation. Tables 3 and 4 show

cost of the piped irrigation system. It is apparent from Table 4 that almost half of the cost is for

the pipe including mains, sub-mains and laterals.

Tables 5 and 6 present results of evaluation of a sprinkler system at different pressures and the

same results are plotted in Figures 1.11 and 1.12. It is apparent from this data that uniformity of

the system depends on operating pressure of the system and fuel consumption increases when the

system is operated at higher pressure. A center-pivot system in maize crop and drip system on

different crops and vegetable are shown in Figures given at the end.

Table 1 Saving in irrigation water using sprinkler irrigation in Pakistan

Crop Water applied (cm) Water saving(%)Furrow/Basin Sprinkler

Turnip 27.18 (F)* 9.4 65.3Pea 19.00 (F) 7.9 58.5

Radish 33.00 (F) 11.7 64.5Maize 25.5 (B)* 13.8 46.0

Average 58.60* Furrow/Basin

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Table 2 Saving in Irrigation Water Using Sprinkler Irrigation in India

Table 3. Comparative Costs of Piped Irrigation Systems

Piped Surface Method Sprinkler Conventionalhand-move

Micro-irrigation solidinstallation

Area (ha) 1 1-2 2-3 1 1-2 2-3 1 1-2 2-3Installationcost(US$/ha)

1700 1600 1400 2800 2700 2100 3950 3300 3000

Annualmaintenancecost(US$/ha)

85 80 70 140 135 105 200 165 150

Note: Average 1997 prices in Europe.Source: (Phocaides, 2000)

Crop Water Applied (cm) WaterSaving (%)

Surface Sprinkler

Bajra 17.78 7.82 56

Jowar 25.40 11.27 56

Cotton 40.64 29.05 29

Wheat 33.02 14.52 56

Barley 17.78 7.82 56

Gram 17.78 7.82 56

Potato 60.00 30.00 50

Average 51.30

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Table 4. Cost breakdown for piped irrigation systems

Component Parts SophisticatedInstallation

SimpleInstallation

Control stationMains, submains and manifoldsFittings and other accessoriesLaterals (pipes and emitters)

> 23%10%22%45%

13%21%24%42%

Source: (Phocaides, 2000)

Some Sprinkler Manufacturer Web Sites

www.senninger.comwww.rainbird.comwww.toro.comwww.orbitonline.comwww.rainforrent.comwww.valmont.com

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Maize on Sprinkler SystemMaize on Sprinkler System

Grapes on Drip irrigation

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Sugarcane on Drip

Chilies on Drip

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Unit 2IRRIGATION SCHEDULING

I. Irrigation Depth

Zax W100

MADd (2.1)

Where, dx is the maximum net depth of water to apply per irrigation; MAD is

management allowed deficit (usually 40% to 60%); Wa is the water holding capacity, a

function of soil texture and structure, equal to FC - WP (field capacity minus wilting

point); and Z is the root depth.

• For most agricultural soils, field capacity (FC) is attained about 1 to 3 days after a

complete irrigation.

• The dx value is the same as "allowable depletion." Actual depth applied may be less if

irrigation frequency is higher than needed during peak use period.

• MAD can also serve as a safety factor because many values (soil data, crop data, weather

data, etc.) are not precisely known.

• Assume that crop yield and crop ET begins to decrease below maximum potential levels

when actual soil water is below MAD (for more than one day).

• Water holding capacity for agricultural soils is usually between 10% and 20% by volume.

• Wa is sometimes called "TAW (total available water), "WHC" (water holding capacity),

"AWHC" (available water holding capacity).

• Note that it may be more appropriate to base net irrigation depth calculations on soil

water tension rather than soil water content, also taking into account the crop type - this is

a common criteria for scheduling irrigations through the use of tensiometers.

II. Irrigation Interval• The maximum irrigation frequency is:

d

xx U

df (2.2)

Where, fx is the maximum interval (frequency) in days; and Ud is the average daily crop water

requirement during the peak-use period.

• The range of fx values for agricultural crops is usually:

0.25 < fx < 80 days (2.3)

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• Then nominal irrigation frequency, f', is the value of fx rounded down to the nearest

whole number of days.

• But, it can be all right to round up if the values are conservative and if fx is near the next

highest integer value.

• f' could be fractional if the sprinkler system is automated.

• f' can be further reduced to account for non-irrigation days (e.g. Sundays), whereby f < f'

• The net application depth per irrigation during the peak use period is dn = f'Ud, which will

be less than or equal to dx. Thus, dn ≤ dx, and when dn = dx, f' becomes fx (the maximum

allowable interval during the peak use period).

• Calculating dn in this way, it is assumed that Ud persists for f' days, which may result in

an overestimation if f' represents a period spanning many days.

III. Peak Use Period

• Irrigation system design is usually for the most demanding conditions:

Figure 2.1 A typical crop coefficient curve

• The value of ET during the peak use period depends on the crop type and on the weather.

Thus, the ET can be different from year to year for the same crop type.

• Some crops may have peak ET at the beginning of the season due to land preparation

requirements, but these crops are normally irrigated by surface systems.

• When a system is to irrigate different crops (in the same or different seasons), the crop

with the highest peak ET should be used to determine system capacity.

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• Consider design probabilities for ET during the peak use period, because peak ET for the

same crop and location will vary from year-to-year due to weather variations.

• Consider deficit irrigation, which may be feasible when water is very scarce and or

expensive (relative to the crop value). However, in many cases farmers are not interested

in practicing deficit irrigation.

IV. Leaching Requirement• Leaching may be necessary if annual rains are not enough to flush the root zone or if deep

percolation from irrigation is small (i.e. good application uniformity and or efficiency).

• If ECw is low, it may not be necessary to consider leaching in the design (system

capacity).

• Design equation for leaching:

we

w

ECEC5

ECLR

(2.4)

where LR is the leaching requirement; ECw is the EC of the irrigation water (dS/m or

mmho/cm); and ECe is the estimated saturation extract EC of the soil root zone for a

given yield reduction value.

• Equation 2.4 is taken from FAO Irrigation and Drainage Paper 29.

• When LR > 0.1, the leaching ratio increases the depth to apply by 1/(1-LR); otherwise,

LR does not need to be considered in calculating the gross depth to apply per irrigation,

nor in calculating system capacity:

a

n

E

dd:0.1LR (2.5)

a

n

LR)E-(1

d0.9d:0.1LR (2.6)

• Ea is the application efficiency in fraction.• When LR < 0.0 (a negative value) the irrigation water is too salty, and the crop would

either die or suffer severely.

• Standard salinity vs. crop yield relationships (e.g. FAO) are given for electrical

conductivity as saturation extract.

• Obtain saturation extract by adding pure water in laboratory until the soil is

saturated, then measure the electrical conductivity.

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• Here are some useful conversions: 1 mmho/cm = 1 dS/m = 550 to 800 mg/l (depending

on chemical makeup, but typically taken as 640 to 690). And, it can usually be assumed

that 1 mg/l « 1 ppm, where ppm is by weight (or mass).

V. Leaching Requirement Example

Suppose ECw = 2.1 mmhos/cm (2.1 dS/m) and ECe for 10% reduction in crop yield is 2.5

dS/m. Then,

20.02.1-5(2.5)

2.1

EC5EC

ECLR

wE

w

(2.7)

Thus, LR > 0.1. And, assuming no loss of water due to application non-uniformity, the gross

application depth is related to the net depth as follows:

LR)-(1

d)(dd n

n dLR (2.8)

nn d25.1

0.20)-(1

dd (2.9)

Gross Application Depth

0.1LRfor,E

dd

pa

n (2.10)

Where, Epa is the design application efficiency (decimal; Eq. 6.9). And,

0.1LRfor,LR)E-(1

0.9dd

pa

n (2.11)

• The gross application depth is the total equivalent depth of water which must be delivered

to the field to replace (all or part of) the soil moisture deficit in the root zone of the soil,

plus any seepage, evaporation, spray drift, runoff and deep percolation losses.

• The above equations for d presume that the first 10% of the leaching requirement will be

satisfied by the Epa (deep percolation losses due to application variability). This presumes

that areas which are under-irrigated during an irrigation will also be over-irrigated in the

following irrigation, or that sufficient leaching will occur during non-growing season

(winter) months.

23

• When the LR value is small (ECw < ECe), leaching may be accomplished both before and

after the peak ET period, and the first equation (for LR < 0.1) can be used for design and

sizing of system components. This will reduce the required pipe and pump sizes because

the "extra" system capacity during the non-peak ET periods is used to provide water for

leaching.

System Capacity

• Application volume can be expressed as either Qt or Ad, where Q is flow rate, t is

time, A is irrigated area and d is gross application depth.

• Both terms are in units of volume.

• Thus, the system capacity is defined as (Eq. 5.4):

fT

AdKQs (2.12)

Where,

Qs = system capacity, l/s (gpm)

T = hours of system operation per day (obviously, T< 24; also, t = fT)

K = coefficient for conversion of units (see below)

d = gross application depth, mm (in.)

f = time to complete one irrigation (days); equal to f' minus the days off

A = net irrigated area supplied by the discharge Qs, ha (acres)

Value of K:

• Metric: for d in mm, A in ha, and Qs in lps: K = 2.78

• English: for d in inches, A in acres, and Qs in gpm: K = 453

24

Notes about system capacity:

• Eq. 2.12 (Eq 5.4 book) is normally used for periodic-move and linear-move sprinkler

systems.

• The equation can also be used for center pivots if f is decimal days to complete one

revolution and d is the gross application depth per revolution.

• For center pivot and fixed systems, irrigations can be light and frequent (dapplied < d):

soil water is maintained somewhat below field capacity at all times (assuming no

leaching requirement), and there is very little deep percolation loss.

• Also, there is a margin of safety in the event that the pump fails (or the system is

temporarily out of operation for whatever reason) just when MAD is reached (time to

irrigate), because the soil water deficit is never allowed to reach MAD.

• However, light and frequent irrigations are associated with higher evaporative losses,

and probably higher ET too (due to more optimal soil moisture conditions).

• Frequent irrigations correspond to a higher basal crop coefficient Kcb (due to more

favorable soil moisture conditions), and a higher wet soil surface evaporation

coefficient, Ks (due to more frequent wetting).

• When a solid-set (fixed) system is used for frost control, all sprinklers must operate

simultaneously and the value of Qs is equal to the number of sprinklers multiplied by

qa. This tends to give a higher Qs than that calculated from Eq. 5.4.

Example: Determine the required system capacity for a sprinkler system with following data:

Area, A = 140 acres root depth, Z = 2 ft

T = 22 h/day Ud = 0.21 in 1 day

MAD = 50 % Cu = 79%

Wa = 1.0 in/ft

1210.5100

ZMAD.Wd a

x

Irrigation Interval, 4)f take,veconservatibe(to4.760.21

1

U

df

d

x

gpm720.7224

1140453

f.T

AdQ

Ks

If f = 5 days gpm577Q s

25

Unit 3WATER DISTRIBUTION UNIFORMITY AND APPLICATION EFFICIENCY

Water Distribution Pattern from a Stationary Sprinkler

Sprinkler head is the most important component of a sprinkle

system because it distributes water over the land. Efficiency and

effectiveness of any sprinkle system depend how uniformly water is

sprayed from the sprinkler.

Water application rate and distribution pattern of a sprinkler

are a function of i) nozzle size and its angle, ii) nozzle pressure, iii)diameter of throw, iv) wind, and v) sprinkler spacing on the lateral and

spacing of the lateral on the main. Water distribution characteristics of sprinkler heads are typical

and change with nozzle- size, shape, angle, and operating pressure. Water application beneath a

sprinkler varies with distance from the head. The pattern of this variation, called distribution

pattern, is usually consistent for a given pressure, nozzle geometry and wind. Pressure has a

significant effect on the distribution pattern. Typical distribution patterns beneath a stationary

impact sprinkler with fixed nozzle geometry for different operating pressures are given in Figure

3.1. If pressure is low, larger water drops fall near the sprinkler forming a 'donut-shaped'

distribution pattern. Under the normal operating pressure as recommended by the manufacturer a

triangular or elliptical shaped distribution pattern is obtained in which the depth of water

application is found maximum near the head and decreases toward the outer edge of the pattern.

Extremely high pressure produces too many fine water drops that fall finer water drops that fall

near the sprinkler distorting the desired distribution pattern (see Fig. 3.2).

Classification of Sprinklers and Applicability

Table 3.1 Classification of sprinkler heads based on operating pressure

Agriculture

sprinklers

(two nozzle)

Nozzle size mm Operating

pressure (bars)

Flow rate

(m3/h)

Diameter

coverage (m)

Low pressure

Medium pressure

High pressure

3.04-4.5x2.5-3.5

4.0-6.0x2.5-4.2

12.0-25.0x5.0-8.0

1.5-2.5

2.5-3.5

4.0-9.0

0.3-1.5

1.5-3.0

5.0-45.0

12-21

24.35

60-80

26

`

Figure 3.1 Water distribution pattern from a stationary rotating sprinkler head(Source: USDA, SCS Handbook, 1960).

Precipitation Profiles• Typical examples of low, correct, and high sprinkler pressures (see Fig 5.5 below).

Figure 3.2 Water Profiles at different Pressures.

27

Analysis of Water Application under a Stationary Sprinkler• Agricultural sprinklers typically have flow rates from 4 to 45 lpm (1 to 12 gpm), at nozzle

pressures of 135 to 700 kPa (20 to 100 psi).

• "Gun" sprinklers may have flow rates up to 2,000 lpm (500 gpm; 33 lps) or more, at

pressures up to 750 kPa (110 psi) or more.

• Sprinklers with higher manufacturer design pressures tend to have larger wetted

diameters.

• But, deviations from manufacturer's recommended pressure may have the opposite effect

(increase in pressure, decrease in diameter), and uniformity will probably be

compromised.

• Sprinklers are usually made of plastic, brass, and or steel.

• Low pressure nozzles save pumping costs, but tend to have large drop sizes and high

application rates.

• Medium pressure sprinklers (210 - 410 kPa, or 30 to 60 psi) tend to have the best

application uniformity.

• Medium pressure sprinklers also tend to have the lowest minimum application rates.

• High pressure sprinklers have high pumping costs, but when used in periodic-move

systems can cover a large area at each set.

• High pressure sprinklers have high application rates.

• Rotating sprinklers have lower application rates because the water is only wetting a

"sector" (not a full circle) at any given instance.

• For the same pressure and discharge, rotating sprinklers have larger wetted diameters.

• Impact sprinklers always rotate; the "impact" action on the stream of water is designed to

provide acceptable uniformity, given that much of the water would otherwise fall far from

the sprinkler (the arm breaks up part of the stream).

The precipitation profile (and uniformity) is a function of many factors:

1. nozzle pressure

2. nozzle shape & size

3. sprinkler head design

4. presence of straightening vanes

5. sprinkler rotation speed

6. trajectory angle

7. riser height

8. wind

• Straightening vanes can be used to compensate for consistently windy conditions.

28

Overlapping sprinkler profiles

Figure 3.3 Water distribution patterns for individual and overlapped sprinklers

(Source: USDA, SCS Handbook, 1960).

Set Sprinkler Uniformity & Efficiency

Sprinkler Irrigation Efficiency

1. Application uniformity

2. Losses (deep percolation, evaporation, runoff, wind drift, etc.)

29

• It is not enough to have uniform application if the average depth is not enough to refillthe root zone to field capacity.

• Similarly, it is not enough to have a correct average application depth if the uniformity is

poor.

• Consider the following examples:

Fig. 3.4 Uniform, but average depth applied exceeds the soil water deficit

(too much deep percolation)

Fig. 3.5 Average depth is correct, but application is highly non-uniform, with

under-irrigation and DP

• We can design a sprinkler system that is capable of providing good application

uniformity, but depth of application is a function of the set time (in periodic-move

systems) or "on time" (in fixed systems).

• Thus, uniformity is mainly a function of design and subsequent system maintenance, but

application depth is a function of management.

30

Quantitative Measures of Uniformity

Traditional measurements of sprinkler irrigation uniformity only account for the aerial

distribution of water.

These measurements of uniformity do not account for redistribution of water within the

soil profile, redistribution due to foliar interception of water drops, and surface runoff

after the drops hit the ground.

Following are two commonly applied indicators of aerial water distribution:

Distribution uniformity, DU (Eq. 6.1):

depthavg

quarterlowofdepthAvg100DU (3.1)

The average of the low quarter is obtained by measuring application from a catch-can

test, mathematically overlapping the data (if necessary), ranking the values by magnitude,

and taking the average of the values from the low ¼ of all values.

For example, if there are 60 values, the low quarter would consist of the 15 values with

the lowest "catches".

Christiansen Coefficient of Uniformity, CU (Eq. 6.2):

n

1j

n

1j j )(zabs0.1100CU

jz

m(3.2)

Where, z are the individual catch-can values (volumes or depths); n is the number of

observations; and m is the average of all catch volumes.

Note that CU can be negative if the distribution is very poor.

There are other, equivalent ways to write the equation.

These two measures of uniformity (CU & DU) date back to the time of slide rules (more

than 50 years ago; no electronic calculators), and are designed with computational ease in

mind.

More complex statistical analyses can be performed, but these values have remained

useful in design and evaluation of sprinkler systems. For CU > 70% the data usually

conform to a normal distribution, symmetrical about the mean value. Then,

31

depthavg

halflowofdepthavg100CU (3.3)

Another way to define CU is through the standard deviation of the values,

2

m0.1100CU (3.4)

Where, is the standard deviation of all values, and a normal distribution is assumed (as

previously)

• Note that CU = 100% for = 0

• The above equation assumes a normal distribution of the depth values, whereby:

2/nm-z (3.5)

• By the way, the ratio /m is known in statistics as the coefficient of variation.

• Following is the approximate relationship between CU and DU:

CU 100 - 0.63(100 - DU) (3.6)

Or

DU 100 -1.59(100 - CU) (3.7)

These equations are used in evaluations of sprinkler systems for both design and operation.

Typically, 85 to 90% is the practical upper limit on DU for set systems DU > 65% and CU >

78% is considered to be the minimum acceptable performance level for an economic system

design; so, you would not normally design a system for a CU < 78%, unless the objective is

simply to "get rid of water or effluent" (which is sometimes the case). For shallow-rooted, high

value crops, you may want to use DU > 76% and CU > 85%.

32

Alternate Sets (Periodic-Move Systems)

• The effective uniformity (over multiple irrigations) increases if "alternate sets" are used

for periodic-move systems (1/2 Sl).

• This is usually practiced by placing laterals halfway between the positions from the

previous irrigation, alternating each time.

• The relationship is:

CUa 10CU (3.8)

DUa 10DU (3.9)

• Use of alternate sets is a good management practice for periodic-move systems.

• The use of alternate sets approaches Sl of zero, which simulates a continuous-move

system.

Uniformity Problems

• From the various causes of non-uniform sprinkler application, some tend to cancel out

with time (multiple irrigations) and others tend to concentrate (get worse).

• In other words, the "composite" CU for two or more irrigations may be (but not

necessarily) greater than the CU for a single irrigation.

1. Factors that tend to Cancel Out

• Variations in sprinkler rotation speed

• Variations in sprinkler discharge due to wear

• Variations in riser angle (especially with hand-move systems)

• Variations in lateral set time

2. Factors that may both Cancel Out and Concentrate

• Non-uniform aerial distribution of water between sprinklers

3. Factors that tend to Concentrate

• Variations in sprinkler discharge due to elevation and head loss

• Surface ponding and runoff

• Edge effects at field boundaries

33

Water distribution uniformity effectively increases after water infiltrates into the soil because

of root-zone redistribution from wetter regions to drier regions. This effect is usually greater

in "tight" clay soils than in sandy soils. Thus, the actual application uniformity in the root

zone tends to be a little better than the aerial distribution from the sprinklers, at least in the

absence of significant runoff.

System Uniformity

• The uniformity is usually less when the entire sprinkler system is considered, because

there tends to be greater pressure variation in the system than at any given lateral

position.

)/P1(2

1CUCUsystem n aP (3.10)

)/P31(4

1DUDUsystem n aP (3.11)

Where, Pn is the minimum sprinkler pressure in the whole field; and Pa is the average

sprinkler pressure in the entire system, over the field area.

These equations can be used in design and evaluation. Note that when Pn = Pa (no

pressure variation) the system CU equals the CU. If pressure regulators are used at each

sprinkler, the system CU is approximately equal to 0.95CU (same for DU). If flexible

orifice nozzles are used, calculate system CU as 0.90CU (same for DU)

The Pa for a system can often be estimated as a weighted average of Pn & Px:

3

P2PP xn

a

(3.12)

Where, Px is the maximum nozzle pressure in the system

DU = f(P,ΔP,S,dn,WDP,WS) (3.31)

Ea = f(P,ΔP,S,dn,WDP,WS,I.is,ti,SWD) (3.32)

34

Fig. 3.6 Due to parabolic loss vs. flow rate relation, the average is closer to Pn

Computer Software and Standards

• There is a computer program called "Catch3D" that performs uniformity calculations on

sprinkler catch-can data and can show the results graphically.

• Jack Keller and John Merriam (1978) published a handbook on the evaluation of

irrigation systems, and this includes simple procedures for evaluating the performance of

sprinkler systems.

• The ASAE S436 (Sep 92) is a detailed standard for determining the application

uniformity under center pivot (not a set sprinkler system, but a continuous move system).

• ASAE S398.1 provides a description of various types of information that can be collected

during an evaluation of a set sprinkler system.

General Sprinkle Application Efficiency

The following material leads up to the development of a general sprinkle application

efficiency term (Eq. 6.9) as follows:

Design Efficiency:

Epa = DEpa Re Oe (3.13)

Where, DEpa is the distribution efficiency (%); Re is the fraction of applied water that

reaches the soil surface; and Oe is the fraction of water that does not leak from the system

pipes.

35

• The design efficiency, Epa, is used to determine gross application depth (for design

purposes), given the net application depth.

• In most designs, it is not possible to do a catch-can test and data analysis you have to

install the system in the field first; thus, use the "design efficiency".

• The subscript "pa" represents the "percent area" of the field that is adequately irrigated

(to dn, or greater). For example, E80 and DE80 are the application and distribution

efficiencies when 80% of the field is adequately irrigated.

Simulate different lateral spacings by "overlapping" catch-can data in the direction of lateral

movement (overlapping along the lateral is automatically included in the catch-can data, unless

it's just one sprinkler).

Figure 3.7 An example to calculate data to measure irrigation uniformity for sprinklerirrigation system using single lateral

Field Evaluation of Sprinklers• Catch-can tests are typically conducted to evaluate the uniformities of installed sprinkler

systems and manufacturer's products.

• Catch-can data is often overlapped for various sprinkler and lateral spacings (Se & Sl) to

evaluate uniformities for design and management purposes.

• A computer program developed at USU does the overlapping: CATCH3D.

• Note that catch-can tests represent a specific wind and pressure situation and must be

repeated to obtain information for other pressures or wind conditions.

36

Se

Sl

• Typical catch-can spacings are 2 or 3 m on a square grid, or 1 to 2 m spacings along one

or more "radial legs", with the sprinkler in the center.

• Set up catch-cans with half spacing from sprinklers (in both axes) to facilitate overlap

calculations.

• See Merriam & Keller (1978); also see ASAE S398.1 and ASAE S436

Choosing a Suitable Sprinkler Heads

• The system designer doesn't "design" a sprinkler, but "selects" a sprinkler.

• There are hundreds of sprinkler designs and variations from several manufacturers, and

new sprinklers appear in the market quite often.

• The system designer must choose between different nozzle sizes and nozzle designs for a

given sprinkler head design.

The objective is to combine sprinkler selection with Se and Sl to provide acceptable application

uniformity, acceptable operating costs, and acceptable hardware & installation costs.

• Manufacturers provide recommended spacings and pressures.

• There are special sprinklers designed for use in frost control.

General Spacing Recommendations• Sprinkler spacing is usually rectangular or triangular.

• Triangular spacing is more common under fixed-

system sprinklers.

• Sprinkler spacings based on average (moderate) wind

speeds:

1. Rectangular spacing is 40% (Se) by 67% (Sl) of the

effective diameter

2. Square spacing is 50% of the effective diameter

3. Equilateral triangle spacing is 62% of the effective

diameter [lateral spacing is 0.62 cos(60°/2) = 0.54,

or 54% of the effective diameter,

• See Fig. 3.8 about profiles and spacings.

• See the following figure about spacings and overlaps.

37

Rectangular: 40% x 67%

Square: 50% x 50%

Triangular: 62% x 54%

Figure 3.8 Overlapping patterns for different spacing of laterals

38

Windy Conditions• When winds are consistently recurring at some specific hour, the system can be shut

down during this period.

• For center pivots, rotation should not be a multiple of 24 hours, even if there is no

appreciable wind (evaporation during day, much less at night).

• If winds consistently occur, special straightening vanes can be used upstream of the

sprinkler nozzles to reduce turbulence; wind is responsible for breaking up the stream, so

under calm conditions the uniformity could decrease.

• For periodic-move systems, laterals should be moved in same direction as prevailing

winds to achieve greater uniformity (because Se < Sl).

• Laterals should also move in the direction of wind to mitigate problems of salt

accumulating on plant leaves.

• Wind can be a major factor on the application uniformity on soils with low infiltration

rates (i.e. low application rates and small drop sizes).

• In windy areas with periodic-move sprinkler systems, the use of offset laterals (Sl) may

significantly increase application uniformity.

• Alternating the time of day of lateral operation in each place in the field may also

improve uniformity under windy conditions.

• Occasionally, wind can help to increase uniformity, as the randomness of wind

turbulence and gusts helps to smooth out the precipitation profile.

Wind effects on the diameter of throw:

0-3 mph wind: reduce manufacturer's listed diameter of throw by 10% for an effective

value (i.e. the diameter where the application of water is significant)

over 3 mph wind: reduce manufacturer's listed diameter of throw by an additional 2.5% for

every 1 mph above 3 mph (5.6% for every 1 m/s over 1.34 m/s)

In equation form:

For 0-3 mph (0-1.34 m/s):

diam = 0.9diammanuf (3.14)

For > 3 mph (> 1.34 m/s):

diam = diammanuf [0.9 - 0.025 (windmph - 3)] (3.15)

or,

diam = diammanuf [0.9 - 0.056(windm/s -1.34)] (3.16)

39

Example: a manufacturer gives an 80-ft diameter of throw for a certain sprinkler and

operating pressure. For a 5 mph wind, what is the effective diameter?

80 ft - (0.10)(0.80) = 72 ft (3.17)

72 ft - (5 mph - 3 mph)(0.025)(80 ft) = 68 ft (3.18)

or,

diam = 80(0.9-0.025(5-3))=68 ft (3.19)

Pressure-Discharge RelationshipEquation 5.1:

q = KdP

where, q is the sprinkler flow rate; Kd is an empirical coefficient; and P is the nozzle pressure

The above equation is for a simple round orifice nozzle. It can be derived from Bernoulli’sequation like this:

2

22

22

P

gA

q

g

V

(3.20)

qPKg

Pd

22gA(3.21)

Where, the elevations are the same (z1 = z2) and the conversion through the nozzle is

assumed to be all pressure to all velocity.

• P can be replaced by H (head), but the value of Kd will be different

• Eq. 5.1 is accurate within a certain range of pressures

• See Table 5.2 for P, q, and Kd relationships

• Kd can be separated into an orifice coefficient, Ko, and nozzle bore area, A:

•

PAKq o (3.22)

Where by,

/2oK (3.23)

Where, the value of Ko is fairly consistent across nozzle sizes for a specific model and

manufacturer.

Application RatesThe application rate should be selected to match conditions of the soil and crop. The

average application rate of a sprinkler can be calculated as:

40

A

qKI (3.24)

Where,

I = application rate (mm/h, in/h)A = wetted area of sprinkler (m2, ft2)K = unit constant (K equal to 60 for I mm/h, q l/min and A m2) or equal to 96.3 for

I in/h, q gpm, and A ft2

A single stationary sprinkler applies water on a circular area. Water depth observe maximumnear the head and decreases outward as shown in Figure 3.1. Thus to obtain a reasonable uniformwater application, the wetted circular areas of adjacent sprinklers are overlapped as shown inFigures 3.2 and 3.3 above. The resulting accumulated depth is almost uniform.

The average application rate along a lateral can be calculated as:

LS

QKI l (3.25)

Where, Ql is the discharge of the lateral, L is the length of lateral, and S is the spacing betweenadjacent lateral, I and K are as previously defined.

Allowable Application RateSprinkle systems are normally designed for no surface runoff. Thus, application rate of a

sprinkle system is designed to apply less water than the infiltration rate of the soil. Complicationarises as the soil infiltration rate decreases with time of application as illustrated by a curve inFigure 3.9.

Figure 3.9 Relationship between infiltration rate of a soil and constant applicationrates.

Infi

ltrat

ion

Rat

e (L

T-1

)

Curve a

b

c

Time (T)

41

Curve in the above figure shows for an unlimited amount of water available at the soilsurface that the infiltration rate is initially higher than the application rate (line b). Thus, norunoff occurs in the beginning of irrigation. As the infiltration rate decreases with time, runoffmay occur if irrigation is continued at rate b. No runoff will occur if the application rate iseverywhere less than curve corresponding to line c.

EVALUATION OF SPRINKLE SYSTEMSIrrigation efficiency and uniformity of water application are often used to describe

effectiveness of any sprinkle system. Keller and Bliesner (1988, page 86) have identified thefollowing factors which affect water application efficiency of sprinkle systems.

Variation of individual sprinkler discharge throughout the lateral lines. This variationcan be held to a minimum by proper pipe network design or by employing pressure orflow-control devices at each sprinkler or sprinkler nozzle.

Variation in water distribution within the sprinkler-spacing area. This variation iscaused primarily by wind. It can be partly overcome for set sprinkler systems by closespacing of the sprinklers. In addition to the variation caused by wind, there is avariability in the distribution pattern of individual sprinklers. The extent of thisvariability depends on sprinkler design, operating pressure, and sprinkler rotation.

Loss of water by direct evaporation from the spray. Losses increase as temperature

and wind velocities increase, and as drop size and application rate decrease.

Evaporation from the soil surface before the water is used by the plants. This loss will

be proportionately smaller as greater depths of water are applied.

UniformityThe performance of any irrigation system is judged by the evenness or uniformity of its

water application. Only an ideal system will apply water with 100 percent uniformity. Forsprinkler systems catch-cans normally placed in a grid pattern are used to estimate the uniformitywith volumes of water collected in the cans measured in graduated cylinders. Christiansen'scoefficient of uniformity, after used to measure the uniformity of application in sprinkleirrigation, is calculated (Christiansen, 1942) from:

]x

-[1.0100CUMN

(3.26)

Where

CU = Christiansen uniformity coefficient in percent,

x = deviation of an individual observation from the mean,

M = mean of all observations, and

N = number of observations

42

The higher the coefficient of uniformity, better the water application of the system will be.

Usually, a system is considered satisfactory if it has a coefficient of uniformity higher than 70

percent.

In the above equation, it is assumed that each catch-can represents an equal sample area.

This is the case in sprinkle systems other than center pivots. For the center pivot system if cans

are set out radially from the pivot point, this would only be true if the can spacing is varied

inversely with the distance from the pivot. Heermann and Hein (1968) suggested a method of

calculating the coefficient of uniformity for the center-pivot system for radially located cans.

They determined the sample area represented by each can and then by considering the volume of

water applied to this area rather than the depth applied at a point, a formula very similar to above

equation was used to calculate the coefficient of uniformity. If the distance between the pivot and

first can is one-half of the distance between the succeeding cans, then the relationship proposed

by Heermann and Hein reduces to the following (Ring and Heermann 1978):

s

ss

RD

DDR

)1(100CU w (3.27)

Where,

CUw = weighted Christiansen coefficient of uniformity,

Ds = depth at any point

D = weighted mean depth, given as

D = (Rs Ds)/ Rs

Rs = weighting factor equal to the distance from the pivot, given as

Rs = 0.5S + (i - 1) S where:

i = subscript referring to the ith can from the pivot

S = spacing between cans

Merriam and Keller (1978) recommended another indicator called Distribution

Uniformity (DU) to measure uniformity. The Distribution uniformity indicates the uniformity

throughout the field and is given by:

Distribution Uniformity = Average low-quarter depth of water applied x 100 (3.28)

Average depth of water applied

The average low-quarter depth is the average of the lowest one-quarter of the data set (assuming

each value represents an equal area) and it does not refer to the lowest one fourth of the field.

The CU and DU are approximately related as (Keller and Bliesner, 1988, p. 87):

CU = 100 - 0.63 (100 - DU) (3.29)

or

DU = 100 - 1.59 (100 - CU) (3.30)

43

Irrigation scheduling and water application practices can be combined to determine the water

application uniformity and efficiency of an irrigation system as shown in the equations below.

DU = f(P,ΔP,S,dn,WDP,WS) (3.31)

Ea = f(P,ΔP,S,dn,WDP,WS,I.is,ti,SWD) (3.32)

Where, P = pressure available at the sprinkler; ΔP = variation of the pressure along the lateral; S= spacings of the sprinklers along and between the laterals; dn = nozzle diameter; WDP = waterdistribution pattern of the sprinkler; WS = wind speed and direction; I= intake characteristics ofthe soil; is = application rate of the sprinkler; ti = duration of the irrigation even; and SWD = soilwater deficit before the irrigation event.

Application EfficiencyEffectiveness of a given sprinkle system can be determined from how much of the

applied water is stored in the crop root zone. Many definitions of application efficiency are foundin the literature therefore the readers are cautioned to use this term carefully. Sometime lesswater is applied than the required soil moisture deficit (SMD) in order to efficiently utilizerainfall. This practice is called under or deficit irrigation. The application efficiency is usuallydefined as:

Ea = Average depth added to the root zone storage x 100 (3.33)

Average depth applied to the field

Data Collection: Data for evaluation of a sprinkle system may be collected while actualsystem is being normally operated. Cans of uniform shape, size and diameter are placed betweenthe sprinklers and laterals in a uniform grid except center-pivot system. First row of cans shouldbe placed at one-half of the grid spacing so that each data point represents equal area. The systemshould be operated for at least one to two hours to collect sufficient water in the containers. Thetest should be conducted during calm day in order to lessen the drift loss due to wind.Evaporation during the test period should also be measured. For this purpose, use cans of thesame size like the one used for collecting catch cans.

If actual system is not in operation, data for DU and CU may be collected by operating afew sprinklers on a lateral. Place the cans between any two sprinklers and note the data asdiscussed above. The uniformity coefficients should be calculated by overlapping the datacollected on the other side of the lateral. If symmetrical conditions are assumed on both side ofthe lateral, data collected even on one side of the lateral may be used to calculate the uniformitycoefficients by overlapping as illustrated in the following example.

Sample Example: A sprinkle system consisting of single lateral was operated to collect data

to calculate uniformity coefficients as shown in Fig. 3.10. Calculate and compare DU and CU for

different lateral spacings.

44

1.0 1.7 3.5 5.0 X 5.1 3.6 2.0 1.0

0.9 2.0 3.7 6.1 5.2 3.9 1.5 0.8

1.0 2.1 3.6 5.5 5.5 4.0 2.0 1.0

0.8 1.8 3.8 5.2 5.6 3.8 1.5 1.0

Figure 3.10 Data collection to measure Distribution Uniformity and Christiansen UniformityCoefficient. Values shown are water depth collected in cans in cm (Grid 3m x 3m).

Calculations are given in Fig. 3.11 for 9 m x 15 m spacings using the above data.

5.1 3.6 2.0 1.0 0.0

0.0 1.0 1.7 3.5 5.0

5.1 4.6 3.7 4.5 5.0

(0.34)* (0.16) (1.06) (0.26) (0.24)

5.2 3.9 1.5 0.8 0.0

0.0 0.9 2.0 3.7 6.1

4.2 4.8 3.5 4.5 6.1

(0.44) (0.04) (1.26) (0.26) (1.34)

5.5 4.0 2.1 1.0 0.0

0.0 1.0 2.0 3.6 5.5

5.5 5.0 4.1 4.6 5.5

(0.74) (0.24) (0.66) (0.16) (0.74)

5.6 3.8 1.5 1.0 0.0

0.0 0.8 1.8 3.8 5.2

5.6 4.6 3.3 4.8 5.2

(0.84) (0.16) (1.46) (0.04) (0.44)

*Figures in parentheses are deviations from the mean.

Figure 3.11 Calculation of Distribution Uniformity and Christiansen Coefficient ofUniformity by Overlapping water depth collected in cm.

X

1.5m 3 m

3 m

Sprinklerhead Lateral

Imaginarylateral

45

There are 20 data points. Mean, M is equal to 4.76 cm. Mean of the lowest one quarter, MLQ is

MLQ = 3.3 + 3.5 + 3.7 + 4.1 + 4.5 = 19.1/5 = 3.82 cm

DU = 3.82/4.76 x 100 = 80.25%

Sum of deviations = 10.72

CU = (1 – 10.72/20 x 4.76) x 100 = 88.74%

Similarly data given in Figure 3.11 may be used to calculate the uniformity coefficients

for other lateral spacings. Table 3.1 summarizes the results for DU and CU for different

spacings. The results in the table shows that the uniformity coefficients decrease as lateral

spacing is increased as expected.

Table 3.2 Measured DU and CU values for different lateral spacings.

Spacings (m)

9 x 12 9 x 15 9 x 18

DU, Percent 89.50 80.25 67.25

CU, Percent 93.20 88.74 75.85

46

C A T C H 3 D Sprinkler Overlap Program

Dr. R.G. Allen, Dept. Ag ansd Irrigation Engr.

Utah State University, Logan, Ut 84322-4105

ph (801) 750-2798

The CATCH3D program is an interactive IBM-PC program written in Microsoft Basic. A

compiled version (CATCH3D.EXE) should be on this disk. CATCH3D is designed to simulate

the water application uniformities of rectangular sprinkler patterns (Se x Sl) by overlapping catch

can measurements from either a single sprinkler head test or single lateral line test.

Sprinkler (Se) and lateral (Sl) spacings evaluated must be integer multiples of the catch can

grid. The catch can grid must be square. In other words, if the catch can grid is 2m by 2m, the

following sprinkler spacings could be evaluated by CATCH3D: 4m x 4m, 4m x 8m, 8m x 4m,

16m x 12m, etc.

Catch can data can be stored by CATCH3D in a data file for future use. Therefore, the data

needs to be typed in only once. Sprinkler and lateral spacings to be evaluated can also be stored

in this same file, along with descriptive information concerning the catch can test: number of

rows and columns of catch-cans, location of the sprinkler, measurement units, catch-can size,

duration of test, nozzle discharge, wind speed and direction, and grid spacing.

Program calculations include estimates of the uniformity coefficient (CU), distribution

uniformity, application efficiencies of the low half and low quarter (AELH, AELQ), and catch

can efficiencies. Example data sets on this disk include CATCH3D.DAT, CONE.DAT and

DONUT.DAT. These files can be read into CATCH3D to provide example calculations and

demonstration of program operation for an actual test, and for synthetic conical and donut shaped

patterns.

The resulting overlapped application patterns can be printed on a line printer, or 3-dimensional

graphs of the patterns can be plotted on the screen (color graphics card with 640x200 resolution

required), or plotted on a Hewlett-Packard 7475A table top plotter. Depicted plots are of a

rectangular overlap section with sprinklers located at each corner of the pattern. To print a copy

of the screen generated 3-d plot onto an Epson-type printer, you must have previously had this

disk (with IBM DOS3.1, GRAPHICS.COM, and AUTOEXEC.BAT) in drive A upon turning on

the computer. Then, after the plot is completed on the computer screen, press the SHIFT and

PRT SC keys simultaneously.

To evaluate a catch-can test from a single lateral with multiple sprinklers, set the sprinkler

spacing (Se) to the actual spacing of the tested lateral, and vary the lateral spacing (Sl) to

evaluate effects of various lateral spacings.

The CATCH3D program is copyrighted, 1986, by the author and by Utah State University.

Neither the author nor Utah State University assumes any liability resulting from use of this

program.

47

Unit 4SPRINKLE IRRIGATION PLANNING AND DESIGN

Hardware Design Process1. Sprinkler selection

2. Design of the system layout

3. Design of the laterals

4. Design of the mainline

5. Pump and power unit selection

Farm Systems vs. Field SystemsA complete farm sprinkle system can be defined as a system planned exclusively for a given

design area or farm unit on which sprinkling will be the primary method of water application.

Planning for complete systems includes considering specified crops and crop rotations, water

quality, and the soils found in the specified design area.

A farm sprinkle irrigation system includes sprinklers and related hardware; lateral, sub-

main, and main pipelines; pumping plant and boosters; operation control equipment; and other

accessories required for the efficient application of water. Large farm systems are made up of

several field systems. A field system is designed either for use on several fields of a farm unit or

for movement between fields on several farm units. Field systems are planned for stated

conditions, generally for pre-irrigation, for bringing up seedlings, or for use on special crops in a

crop rotation.

`"A poorly designed system that is well managed can often perform better than a well

designed system that is poorly managed"

• A Farm system may have many field systems.

• Planning considerations should include the possibility of future expansions and extra

capacity.

• Permanent buried mainlines should generally be oversized to allow for future needs. It is

much cheaper to put a larger pipe in at the beginning than to install a secondary or larger

line later.

• Consider the possibility of future automation.

• Consider the needs for land leveling before burying pipes.

• How will the system be coordinated over many fields?

• What if the cropping patterns change? (tolerance to salinity, tolerance to foliar wetting,

peak ET rate, root depth, need for crop cooling or frost protection, temporal shifting of

peak ET period).

• What if energy costs change?

• What if labor availability and or cost change?

48

• What if the water supply is changed (e.g. from river to groundwater, or from old well to

new well)?

• What if new areas will be brought into production?

II. Outline of Sprinkler Design Procedure1. Make an inventory of resources

• Visit the field site personally if at all possible, and talk with the farmer.

• Get data on soil, topography, water supply, crops, farm schedules, climate, energy, etc.

• Be suspicious of parameter values and check whether they are within reasonable

ranges.

2. Calculate a preliminary value for the maximum net irrigation depth, dx.

3. Obtain values for peak ET rate, Ud, and cumulative seasonal ET, U (Table 3.3).

4. Calculate maximum irrigation frequency, fx, and nominal frequency, f'.

• This step is unnecessary for automated fixed systems and center pivots.

5. Calculate the required system capacity, Qs

• first, calculate gross application depth, d

• for center pivots use dn/f = Ud, and T « 90% of 24 hrs/day = 21.6

6. Determine the "optimum" (or maximum) water application rate.

• a function of soil type and ground slope (Table 5.4).

7. Consider different types of feasible sprinkle systems.

8. For periodic-move and fixed (solid-set) systems:

(a) Determine Se, qa, nozzle size, and P for optimum application rate (Tables 6.4 to 6.7)

(b) Determine number of sprinklers to operate simultaneously to meet Qs (Ns = Qs/qa)

(c) Decide upon the best layout of laterals and mainline

(d) Adjust f, d, and/or Qs to meet layout conditions

(e) Size the lateral pipes

(f) Calculate the maximum pressure required for individual laterals

9. Calculate the mainline pipe size(s), then select from available sizes.

10. Adjust mainline pipe sizes according to the "economic pipe selection method" (Chapter 10),

and check velocity limits too.

11. Determine extreme operating pressure and discharge conditions.

12. Select the pump and power unit.

13. Draw up system plans and make a list of items with suggestions for operation and

maintenance of the hardware.

III. Summary• Note that MAD is not a precise value; actual precision is less than two significant digits;

this justifies some imprecision in other values (don't try to obtain very precise values for

some parameters when others are only rough estimates).

49

• When determining the seasonal water requirements we subtract Pe from U. However, to

be safe, the value of Pe must be reliable and consistent from year to year, otherwise a

smaller (or zero) value should be used.

• Note that lateral and sprinkler spacings are not infinitely adjustable: they come in

standard dimensions from which designers must choose. The same goes for pipe

diameters and lengths.

• However, buried PVC pipes in a fixed system can be cut to any length during installation,

allowing for a great deal of flexibility.

• Note that design for peak Ud may not be appropriate if sprinklers are used only to

germinate seeds (when later irrigations are by a surface method).

Sprinkle System DesignDesign of a sprinkle system starts with layout of laterals and main pipelines. Pipe layout

may be simple for small regularly shaped fields to complex for large and odd-shaped areas.

Layout mainly depends on field topography, lateral settings, wind conditions and location of

water source. Design of set move, solid set gun sprinkler and center-pivot are discussed briefly.

For more details, the reader is referred to Keller and Bliesner (1990), Pair et al. (1975), Rolland

(1982), and other sources.

Set-Move and Solid Set SystemsMain steps to design a set-move or solid set sprinklers are layout of main pipe lines and

laterals, determining the number of laterals to be operated per irrigation, number of sprinkler

heads to be operated, discharge required and pump characteristics.

System LayoutLayout of the system mainly depends on topography, field size and shape, location and

source of water supply.

Required System CapacityThe capacity of a sprinkle system depends on the area to be irrigated; the gross depth of

water required for each irrigation, time allowed completing irrigation during peak water use

period, f and actual operating time per day. The capacity can be calculated by the equation as:

fT

AdKQs (4.1)

Where,

Qs = discharge capacity, l/s (gpm)

K = conversion constant, 2.78 for metric and 453 for English units

50

A = design area, ha (acres)

d = gross irrigation depth, mm (in)

f = operating time allowed to complete one irrigation, days

T = actual operating time per day, h/day

For a given area, d, f and T have significant impact on the system capacity. Greater the irrigation

depth, larger will be the system capacity. For a given depth, d, greater the operating time (IT),

the smaller will be the system capacity and vice versa. The operating time, f should be one to two

days less than the irrigation cycle during peak water use period. Similarly T should be at least 5

to 10 percent less than 24 hours.

Number of SprinklersNumber of sprinklers operating at one time can be calculated as:

a

s

q

QsN (4.2)

Where,

Ns = number of sprinklers operating

Qs = total system discharge, L/s (gpm)

qa = average sprinkler discharge, L/s (gpm)

Variation in the number of operating sprinklers should be kept to minimum but it may be

sometime unavoidable at the end of an irrigation cycle. On the last day of irrigation, only a few

laterals may be needed to complete the irrigation.

Number of Laterals Operated per SetLength of laterals may be determined by deciding the final layout of the system. Dividing

the lateral length by the spacing between the sprinkler heads on the lateral will give the number

of sprinklers operating on the lateral.

Divide the total minimum number of sprinklers required by the number of sprinklers on

one lateral to get the minimum number of lateral required. The above computations are finally

adjusted as illustrated in the following example:

51

Sample Example 4.1: Computing system capacity requirements for a single crop in the design

area.

Given: Field of corn, A = 16 ha

Design moisture use rate, Ud = 5 mm/day

Moisture replaced in soil at each irrigation, dn = 60 mm

Irrigation efficiency, Ea = 75%

Irrigation period, f = 10 days in a 12-day interval

System operating time per day, T = 20 hr/day

Electrical conductivity of the irrigation water, ECw = 2.1 dS/m

Calculations: Leaching requirements can be calculated by using the following equation:

100/ELR)-(1.0

d0.9d

a

n

in)(3.54mm90100/750.20)-(1.0

600.9d

Using the equation to compute the system capacity:

Qs = 2.78 AdfT

gpm)(317L/s20.02010

90162.78

Sample Example 4.2:A side roll sprinkle system is to be designed for the field shown below;

laterals will operate on both sides of the main line.

Pump

(in center)

1200

ft

2100 ft

Mai

nlin

e

52

The following data is for the preliminary design:

qa = 3.8 gpm/sprinkler f = 5 days

Se = 30 feet/sprinkler d = 1.11 inches

S1 = 40 feet/position T = (3 sets/day) x (4 hrs/set)

1. What is the preliminary system capacity (gpm)?

(There are 43,560 sq ft/acre)

2. How many sprinklers will be operating simultaneously?

(Round to the nearest whole number)

3. How many sprinklers per lateral?

4. How many lateral(s) will be needed?

5. How many sets for each of the lateral(s)?

6. What is the adjusted system capacity (gpm)?

Solution:

1. gpm484.82512

1.11

43560

12002100453

T.f

AdKQsinitial

2. 128127.583.8

484.82

q

QN

a

ss

3. Sprinkler per lateral = 3530

1050

4. No. of laterals needed = 465.335

128

5. Settings of laterals = main theofsideeachon3040

1200

- If 1 lateral is operated, field will be irrigated in = 60/3 = 20 days

- 2 “ 60/3 = 20 days- “ 60/6 = 10 days

- 3 “ 60/9 = 7 days- 4 “ 60/12 = 5 days

Therefore 4 laterals are needed (20 each side of the main line)Therefore setting of each lateral = 600/40 = 156. Adjusted Qs = (No. of laterals) 4 x 35 x qa = 4 x 35 3.8 = 532 gpm

53

Layout of Laterals for Set Sprinklers

I. Selecting Sprinkler Discharge, Spacing, and Pressure

• In Chapter 6 of the textbook there are several tables that provide guidelines for nozzle

sizes for different:

• Wind conditions

• Application rates

• Sprinkler spacings

• For selected values of wind, application rate, and spacing, the tables provide

recommended nozzle sizes for single and double-nozzle sprinklers, recommended

sprinkler pressure, and approximate uniformity (CU).

• Table values are for standard (non-flexible) nozzles.

• Table values are for standard sprinkler and lateral spacings.

• More specific information can be obtained from manufacturer's data.

• Recall that the maximum application rate is a function of soil texture, soil structure, and

topography (Table 5.4).

• For a given spacing and application rate, the sprinkler discharge, qa, can be determined

from Eq. 5.5.

to

Ie

S

SSI

pa

Iena E3600

SSd

3600

)(q (4.3)

Where, qa is in lps; I is in mm/hr; dn is in mm; Sto is the operating time for each set, in

hours; Se and Sl are in m and Epa is application efficiency.

II. Number of Operating Sprinklers

• After calculating the system capacity and the design flow rate for sprinklers, the number

of sprinklers that will operate at the same time is:

a

ss q

QN (4.2)

Where, Ns is the minimum number of sprinklers operating, and Qs and qa have the same

units.

54

• It is recommendable to always operate the same number of sprinklers when the system is

running. This practice can help avoid the need for pressure regulation, and can avoid

uniformity problems. It can also help avoid wasting energy at the pump.

• For odd-shaped fields, and sometimes for rectangular fields, it is not possible to operate

the same number of sprinklers for all sets. In this case, pressure regulation may be

necessary, or other steps can be taken (multiple pumps, variable-speed motor, variable

application rates).

III. Lateral Design Criteria

• Lateral pressure varies from inlet to extreme end due to:

1. friction loss

2. elevation change

• The fundamental basis upon which sprinkler laterals are designed is:

"Pressure head variation in the lateral should not exceed 20% of the

average design pressure for the sprinklers"

• This is a design assumption that has been used for many years, and is based on a great

deal of experience.

• The 20% for pressure variation is not an "exact" value; rather, it is based on judgment and

some cost comparisons.

• A designer could change this value, but it would affect system performance (uniformity),

initial system cost, operating cost, and possibly other factors.

• Computer programs could be written to search for an "optimal" percent pressure variation

according to initial and operating costs, and according to crop value -- such an "optimal"

value would vary from system to system.

IV. Sprinkler Lateral Orientation

• It is usually preferable to run laterals on contours (zero slope) so that pressure variation in

the lateral pipes is due to friction loss only.

• It is advantageous to run laterals downhill, if possible, because the gain in energy due to

elevation change will allow longer laterals without violating the 20% rule. But, if the

slope is too steep, pressure regulators or flow control nozzles may be desirable.

55

• If the ground slope is equal to the friction loss gradient, the pressure in the lateral will be

constant.

• However, the friction loss gradient is nonlinear because the flow rate is decreasing withdistance along the lateral.

Figure 4.1 An example of pressure drop on zero slope, downhill and uphill lateral positions.

Lateral

Ground

56

It is usually not recommendable to run laterals in an uphill direction. In this case:

1. Both friction loss and elevation are working to reduce pressure toward the end of

the lateral, and length is more restricted if the 20% rule is still used.

2. However, for small slopes, running laterals uphill may be required to reduce the

total length of the mainline pipe.

• Note that V2/2g in the lateral pipe is normally converted into total head as the water flows

through the nozzle body. Therefore, the velocity head (and EL) should normally be

considered in lateral design. However, since a portion of the velocity head is lost during

deceleration of the water at the entrance into risers and as turbulence inside the sprinkler

head, and since V2/2g in a lateral pipe is typically small (< 1 ft of head, or 0.2 psi, or 0.3

m head, or 3 kPa), it is normally neglected during design, and the HGL is used.

• Aside from limits on pressure variation, laterals should be oriented so that they move in

the direction of the prevailing winds this is because of salinity problems and application

uniformity.

• Figure 4.2 gives examples of layouts on different topographies.

Topography: Topography of the field greatly affects layout of main pipeline and laterals. As a

general rule, the lateral should be laid across the slope and pressure variation along a lateral

should not exceed 20% of the average design operating pressure (Keller and Bliesner (1990;

page 126). Variation in discharge along a lateral should be minimum and normally variation in

discharge should not exceed 10%.

Layouts of main lines and laterals for different field topography are shown in Fig. 4.2.

Note that there may be a number of pipe layouts possible but the best one should be selected

based on above principles of pressure and discharge variations. To meet these requirements, the

laterals should be laid on the contours or across prominent field slopes (Figure. 4.2 a, b & c). The

lateral length should be limited to that length in which the friction loss does not exceed 20% of

the designed operating pressure. Running laterals uphill should be avoided as far as possible. If

this situation is unavoidable, then use shorter lateral on the uphill side. Pressure and flow

regulators should be used to avoid excessive variation in pressure or discharge respectively.

Longer laterals may be used if they are laid down the slope. Under this condition,

difference in elevation in both ends of the lateral results gain in pressure head. Thus longer

laterals may be used than the similar one lay on level field (Fig. 4.2 d, e, f). Two main-lines are

laid in Figure 4.2 to avoid running the laterals uphill.

57

Figure 4.2 Layout of laterals for periodic-move sprinkle system withdifferent topographic conditions (Source: Keller and Bliesner,1990; page 125)

58

V. Lateral Sizing Limitations

• Lateral pipes can be designed with multiple diameters to accommodate desirable pressure

distributions, but...

• Hand-move laterals should have only one or two different pipe sizes to simplify handling

during set changes.

• In practice, hand-move systems and wheel lines usually have only one size of lateral

pipe.

• Some wheel lines, greater than 400 m in length, may have 5-inch pipe near the inlet and

then 4-inch pipe at the end.

Layout of Mainline for Set Sprinklers

I. Mainline Layout and Sizing

• If possible, run the mainline up or down slope so the laterals can be on contours (lateral

pressure variation due to friction loss only).

• Can also run the mainline along a ridge so the laterals run downhill on both sides (lateral

friction loss partially offset by elevation change).

• Should consider possible future expansions when sizing the mainline.

"Split-Line" Lateral Operation:

• Laterals operate on both sides of the mainline.

• The mainline can be sized for only half capacity halfway down the mainline if laterals are

run in different directions.

• Sometimes interferes with cultural practices.

• It is convenient to have the water supply in the center of one side of the field, but this is

seldom a design variable (the well is already there, or the canal is already there).

• May not need pumping if the water supply is at a higher elevation than the field elevation

(e.g. 50 psi = 115 ft or 35 m of head) when pumping is not required, this changes the

mainline layout and pipe sizing strategy.

• In some cases it will be justifiable to include one or more booster pumps in the design --

even when the water source is a well (the well pump may not provide enough pressure for

any of the lateral settings).

II.Design Variables to Accommodate Layout

• Number of sprinklers operating• Average application rate

59

• Gross application depth

• Average sprinkler discharge

• Sprinkler spacing

• Operating hours per day

• Irrigation frequency

• Total operating time (fT)

• System capacity

• Percent probability of rain during peak-use period

• MAD

• It may be necessary to adjust the layout if a suitable combination of the above variables

cannot be found.

• Can also use flow control nozzles or pressure regulators to accommodate a given layout.

Sample Example 4.3:

• Consider a periodic-move system with Sl = 50 ft, Se = 40 ft, f = 8 days, T = 11.5 hrs @ 2

sets/day, d = 2.7", and qa = 4.78 gpm

• The field size is 80 acres (% of a "quarter section"), 2,640 ft on one side and 1,320 ft on

the other, rectangular

• The laterals will have to be 1,320 ft long

System capacity:

gpm532hrs/set)11.5sets/day)((2days)8(

inch)(2.7ac)80(453Qs (4.4)

Number of sprinklers operating:

sprinklers11178.4

532N s

a

s

q

Q(4.5)

• Number of laterals,

/lateralssprinklers33erft/sprinkl40

ft/lateral1320 (4.6)

laterals3.36/lateralsprinklers33

sprinklers111 (4.7)

so, round up to 4 laterals

60

• Thus, two laterals on each side of the mainline (symmetry)

26.4nft/positio50

pairlateralperft1320 (4.8)

• Round this up from 26.4 to 27 positions per lateral pair.

• This gives 2 x 27 = 54 total lateral positions, and 54/4 = 13.5 sets/lateral.

• Use 13 sets for two laterals and 14 sets for the other two laterals.

• Then, there will be 14 sets per irrigation, even though the last set will only have two laterals

operating.

• Adjusted irrigation frequency:

days7sets/day2

sets14f (4.9)

Note that the value of f was for an 8-day interval

Thus, we need to increase Qs to complete the irrigation in less time

Adjusted system capacity:

Qs = (4 laterals)(33 sprinklers/lateral)(4.78 gpm/sprinkler) (4.10)

= 631gpm

Another way to adjust the system capacity:

61

gpm608gpm)(532days7

days8Qs

(4.11)

You might say that we are "effectively" finishing in somewhat less than 7 days, because

the last set has only two laterals in operation, giving a system capacity of 608 instead of

631.

Consider this calculation: there are 2 x 13 + 2 x 14 = 54 sets, but the last 2 sets have only

2 laterals, so, (52/54) x 631 = 608 gpm, as calculated above. Which is correct?

There is (52/54)*(4 laterals) = 3.85 laterals operating on average during each irrigation of

the field. However, you cannot always base the system capacity on the average number of

laterals operating.

The system capacity should be based on the "worst case", which is when all four laterals

operate simultaneously.

This means that the required capacity is 631 gpm, not 608 gpm.

Note that many farmers will accept some increase in system capital cost to provide more

operational flexibility and safety.

In summary, we have essentially lowered f (irrigation frequency) to accommodate the

system configuration (layout), but:

• same gross depth

• same number of hours per set

• same sprinkler flow rate

• same sprinkler spacing

• increased system capacity

Sample Example 4.4: A field measuring 800 m x 400 m is considered for designing a sprinkle

system. Field data indicates that irrigation depth of 5 cm should be applied weekly during peak

water use period. There will be two 11 hours settings per day. It is desirable to complete the

irrigation in six days allowing one day for maintenance of the system and other farming activities

qa = 20 lpm and sprinkler spacing = 15 x 20 m2. Assume it is not desirable to use lateral longer

than 400 m in this example.

Calculations:

L/s33.7226

50

10,000

4008002.78

fT

AdKQs

Total number of sprinklers, Ns = Qs/1 = 33.7 = 10120/60

62

Number of sprinkler per lateral = 400/15 = 26.66 ≈ 27

Minimum whole number of laterals required = 102/27 = 3.8 ≈ 4

The number of lateral positions on each side of the main line with S1 = 20 m is:

= 400/20 = 20 position

Total numbers of lateral positions on both sides of the main line are 20 x 2 = 40. Thus four

laterals with two settings per day will cover the field in 5 days. Thus design is conservative and

the whole field will be irrigated in five days instead of six days.

Final adjustment: With four laterals operating simultaneously, the maximum number of

sprinklers running is:

Nsp = 4 x 27 = 108

Actual discharge of the system should be = 108 x 20/60 = 36 Lps

Mainline with 20 hydrants at 20 m 0

0

0

0

0

0

0

0

Lateral with 27 sprinklers

Number of sprinkler operating = 27 x 4 =

108

System capacity = 36 lps

400 m

800 m

Figure 4.3 Sprinkler system’s layout in 800 m x 400 mm field.

Sample Example 4.5: Calculations for a Periodic-Move SystemGiven:

Crop is alfalfa. Top soil is 1.0 m of silt loam, and subsoil is 1.8 m of clay loam. Field area is

35 ha. MAD is 50% and ECw is 2.0 dS/m. Application efficiency is estimated at 80%, and the

soil intake rate is 15 mm/hr. Lateral spacing is 15 m and lateral length is 400 m. Assume it

takes 1/2 hour to change sets. Seasonal effective rainfall is 190 mm; climate is hot. Assume

one day off per week (irrigate only 6 days/week).

From tables in the textbook:Hot climate, table 3.3 gives ................Ud = 7.6 mm/day, and U = 914 mm/season

Top soil, table 3.1 gives .....................................................................Wa = 167 mm/m

Sub soil, table 3.1 gives .....................................................................Wa = 183 mm/m

63

Root depth, table 3.2 gives ................................................. Z = (1.2 + 1.8)/2 = 1.5 m

Salinity for 10% yield reduction, Table 3.5 gives ..............................ECe = 3.4 dS/m

1. Average water holding capacity in root zone:

top soil is 1.0 m deep; root zone is 1.5 m deep...

mm/m3.1725.1

)183)(0.15.1()167(0.1Wa

(4.12)

2. Max net application depth (Eq. 3.1):

mm129.25)(172.3)(1.100

50Z W

100

MADd ax

(4.13)

3. Maximum irrigation interval (Eq. 3.2):

days17.0mm/day7.6

mm129.2

U

Uf

d

xx (4.14)

4. Nominal irrigation interval (round down, or truncate):

f’ = trunk (fx) = 17 days (4.15)

5. Net application depth:

dn = f'Ud = (17 days)(7.6 mm/day) = 129.2 mm (4.16)

6. Operating time for an irrigation:

17 days is just over two weeks, and depending on which day is off, there could be 3 off

days in this period. So, with one day off per week, we will design the system capacity to

finish in 17 - 3 = 14 days. Thus, f = 14 days. But, remember that we still have to apply 17

days worth of water in these 14 days (we irrigate 6 days/week but crop transpires 7

days/week).

7. Leaching requirement (Eq. 3.3):

13.02.0-5(3.4)

2.0

EC5EC

ECLR

wE

w

(4.17)

64

LR > 0.1; therefore, use Eq. 5.3 b...8. Gross application depth (Eq. 5.3b):

mm167.10.13)(0.8)-(1

0.9(129.2)

)100/LR)(E-(1

0.9dd

a

n (4.18)

9. Actual set operating time:

With 167.1 mm to apply and a soil intake rate of 15 mm/hr, this gives 11.14 hrs minimum

set time (so as not to exceed soil intake rate). Then, we can make the nominal set time

equal to 11.5 hours for convenience. With 0.5 hrs to move each set, there are a total of

12.0 hrs per set, and the farmer can change at 0600 and 1800 (for example).

At this point we could take the sprinkler spacing, Se, lateral spacing, Sl, and actual

application rate to determine the flow rate required per sprinkler.

10. Sets per day:

From the above, we can see that there would be two sets per day.

11. Number of sets per irrigation:

(14 days/irrigation)(2 sets/day) = 28 sets

12. Area per lateral per irrigation:

Lateral spacing on mainline is Sl = 15 m. Lateral length is 400 m. Then, the area per

lateral is:

(15 m/set)(28 sets)(400 m/lateral) = 16.8 ha/lateral

13. Number of laterals needed:

35 ha/16.8 ha/lateral = 2.08 laterals (4.19)

Normally we would round up to the nearest integer, but because this is so close to 2.0 we

will use two laterals in this design.

14. Number of irrigations per season:

(U - Pe)/dn = (914 mm - 190 mm)/129.2 mm/irrig = 5.6 irrigations

Thus, it seems there would be approximately six irrigations in a season. But the initial Rz

is less than 1.5 m, so there may be more than six irrigations.

65

15. System flow capacity (Eq. 5.4):

with 11.5 hours operating time per set and two sets per day, the system runs 23 hrs/day...

fT

Ad2.78Qs (4.1)

hrs/day)(23days)(14

mm)(167.1ha)(352.78Qs

= 50.5 lps (800 gpm)

This is assuming no effective precipitation during the peak ET period, so the design should be

conservative.

66

Unit 5PIPELINE HYDRAULICS, FRICTION LOSSES AND DESIGN OF LATERALS

Pressure and Pressure VariationsWater must be applied at suitable pressure for good performance of all sprinkle

systems. In a stationary container, pressure at any depth is same everywhere and is equal to

the product of the unit weight of water 1000 kg/m3 at 20oC (62.4 lb/ft3 at 60oF) and the height

of water above that point. Height of water in the column is called the head. Note that

diameter of the pipe or shape of container has no effect on pressure. Pressure is usually

expressed in kilopascals, kPa (pounds per square inch, psi) and head is expressed in m (ft) of

water. One kPa (psi) of pressure is equal to 0.102 m (2.31 ft) of water head or 1 m of pressure

head is equivalent to 9.8 kPa of pressure. In a sprinkle system, pressure or head consists of

different components: static head, pressure head, velocity head, friction head and elevation

head above a datum point.

Dynamic Head: The operating head of a sprinkle system consists of different

components as discussed below:

i) Total Static Head: Static head is equal to the difference in elevation between the

highest discharge point and the reference point. The distance from the water surface to the

center line of pump is called static suction head. If water supply is from a well or sump, there

may be excessive suction due to drawdown. Sum of static head and suction is called the total

static head.

Pressure Head: The pressure head is necessary to spray water through the sprinkler

nozzle which converts the pressure head into velocity head that carries the water away from

the sprinkler.

Velocity Head: Velocity of water in a sprinkler system seldom exceeds 2.5 m (8 ft) per

second. Therefore, the velocity head may be neglected except in computing suction head for

centrifugal pumps.

Friction Head: The pressure drops when water flows through the pipes and pipe

fittings. Sudden increase or decrease in pipe diameter also cause drop in pressure. This loss in

pressure is called friction head. Hazen-Williams equation is commonly used to calculate

friction head loss in sprinkle and trickle systems which is:

4.871.852

1.852f D

(C)

(Q)K

L

100hJ (5.1)

Where

J = head loss gradient, m/100 m (ft/100 ft)

K = conversion constant, 1.217 x 1012 for metric units (1050 for English units)

hf = head loss due to pipe friction, m (ft)

67

L = length of pipe, m (ft)

Q = flow rate in the pipe, L/s (gpm)

C = friction coefficient, which is a function of pipe material characteristics

D = inside diameter of the pipe, mm (in.)

Typical values of C for use in the Hazen-Williams equation are:

Pipe Material C

Plastic 150

Epoxy-coated steel 145

Cement asbestos 140

Galvanized steel 135

Aluminum (with couplers every 30 ft) 130

Steel (new) 130

Steel (15 years old) or concrete 100

Source: (Keller and Blisner, 1988, page 135)

For smooth plastic pipes, Watters and Keller (1978) proposed the following equations as

discussed by Keller and Bliesner (1988, page 138):

J = 100 hf/L = K Q1.75/D4.75 (for D < 125 mm) (5.2)

and

J = 100 hf/L = K Q1.83/D4.83 (for D > 125 mm) (5.3)

Where, K and K1 are conversion constants. K = 7.88 x 107 for metric units (0.133 for English

units, and K1 = 9.58 x 107 for metric units and 0.100 for English units). Other symbols are as

defined above.

For pipe friction loss, use the Hazen-Williams and Darcy-Weisbach equations

We can use the Swamee-Jain equation instead of the Moody diagram to determine the

f value i.e.

9.010 R

74.5

D75.3log

0.25f

y

(5.4)

Which is valid for turbulent flow in the range: 4,000 < Ry < 1.0(10)8, where Ry is the

Reynolds number.

The ratio ε/D is called "relative roughness".

68

The roughness height, ε, varies widely according to pipe material and

condition/age.

Use the Blasius equation (Eq. 8.6) to determine the value of "f," in some cases, for

"smooth pipes" (e.g. plastic pipes) which is:

Ff = 0.32 Ry-0.25 (5.5)

Where, Ff is the Darcy-Weisbach pipe friction factor. The Ff is related to the head loss in the

pipe, hf by the Darcy-Weisbach equation as:

2g

V

D

LFh

2

ff (5.6)

Where

V = Velocity of flow in the pipe, (m/s) (ft/s)

g = Acceleration due to gravity, 9.81 m/s2 (32.2 ft/s2)

D = Inside pipe diameter, m (ft)

Hazen-Williams Equation

This is a simple, empirical pipe friction-loss equation:

100

JLh f (5.7)

Where hf is the friction loss (head of water); L is the pipe length; and,

4.87-852.1 D)C

Q(KJ (5.8)

In which Q is the flow rate; C is a roughness coefficient; and D is the pipe inside diameter.

• The value of K in this equation is:

K = 1,050 for Q in gpm and D in inches

K = 16.42(10)6 for Q in lps and D in cm

K=1.217(10)12 for Q in lps and D in mm

Darcy-Weisbach Equation

• This is a (usually) more accurate pipe friction-loss equation:

2gD

LVFh

2

ff (5.9)

Where Ff is usually determined from Eq. 4, or from the Blasius equation (see below).

69

Blasius Equation

• This can be used to estimate the Ff value for smooth (e.g. plastic) pipes of the typical

diameters found in pressurized irrigation systems:

-0.25yf R0.32F (5.10)

Where, 2,000 < Ry < 100,000

Sample Example: Computation of friction losses

Given: A 100 mm (4 in) aluminum lateral pipeline 396 m long with 12 m between outlets and

sprinklers discharging 30 L/min. (The inside diameter of the pipe is 99 mm).

Calculations: The number of sprinklers: N= 400/12 = 33.33 (round no. 33)

The lateral discharge is:

QI = 33 x 30 = 990 L/min = 16.5 L/s

And using the equation (8)

5.06)99(130

5.1610 x1.21J 87.4

852.112

And by Eq. (1) with F = 0.36 from Table 8.7:

kPa70.7m7.21100

3960.36 x5.06h f

Set Sprinkler Lateral DesignI. Basic Design Criterion

1. The basic design criterion is to size lateral pipes so that pressure variation along thelength of the lateral does not exceed 20% of the nominal design pressure for thesprinklers.

2. This criterion is a compromise between cost of the lateral pipe and application

uniformity in the direction of the lateral.

3. Note that the locations of maximum and minimum pressure along a lateral pipe can vary

according to ground slope and friction loss gradient.

4. For laterals on level grounds, change in ΔPe = 0.0 (ΔHe =0.0), and the allowable pressure

loss due to friction in the lateral line will be equal to 20% of Pa (average pressure).

5. For uphill laterals (see Figure 9.2a) Pf (pressure loss due to friction) may be equal to 20%

of Pa minus the static pressure difference due to elevation, ΔPe, which is the difference in

elevation between the inlet and closed ends of the lateral.

6. For uphill lateral, the minimum pressure, Pn (nominal pressure) occurs at the closed end

of the pipeline.

70

7. For downhill laterals the allowable pressure Pf is 20% of Pa plus the static pressure gain

due to the decrease in elevation between the inlet and closed ends of the laterals.

8. For downhill laterals Pn occurs at the point along the lateral where the pipe friction

gradient equals the slope of the lateral (ground as shown in Figure 9.2b).

II. Location of Average Pressure in the Lateral

We are interested in the location of average pressure along a lateral pipe because it is related

to the design of the lateral. Recall that friction head loss along a multiple-outlet pipe is

nonlinear. The figure below is for a lateral laid on level ground - pressure variation is due to

friction loss only.

Figure 5.1. Example of pressure drop in a multiple outlet pipe (lateral)

For equally-spaced outlets (sprinklers) and approximately thirty outlets (or more), three-

quarters of the pressure loss due to friction will occur between the inlet and the location of

average pressure.

The location of average pressure in the lateral is approximately 40% of the lateral length,

measured from the lateral inlet.

If there were only one outlet at the end of the lateral pipe, then one-half the pressure loss due

to friction would take place between the lateral inlet and the location of average pressure, as

shown below.

71

Figure 5.2. Pressure Drop for one outlet at end of the lateral

• Consider the following equations:

Total friction head loss:

n

1i iftotalf )(h)(h (5.11)

1n

)(h)(h

n

1i

i

1j jf

af (5.12)

where n is the number of sprinklers; (hf)total is the total friction head loss from 0 to L; (hf)i

is the friction head loss in the lateral pipe between sprinklers i-1 and i; and (hf)a is the

friction loss from the lateral inlet to the location of ha.

• As indicated above, (hf)a occurs over approximately the first 40% of the lateral.

• Note that between sprinklers, the friction head loss gradient is linear in the lateral pipe

with one outlet at the end.

• Note also that (hf)0 = 0, but it is used in calculating (ha)f, so the denominator is (n+1), not

n.

Friction head loss to location of ha:

72

Figure 5.3 Pressure losses are non-linear in a multiple outlet lateral

In applying these equations with sample data, the following result can be found (see

example 9.1 in the text).

0.73)(h

)(h

totalf

af (5.13)

• This supports the above claim that approximately 3/4 of the friction head loss occurs

between the lateral inlet and the location of ha.

• Also, from these calculations it can be seen that the location of ha is approximately

38% of the lateral length, measured from the inlet, for laterals with approximately 30

or more sprinklers.

• But, this analysis assumes a constant qa, which is not quite correct unless flow control

nozzles and or pressure regulators are used at each sprinkler.

• We could eliminate this assumption of constant qa, but it involves the solution of a

system of nonlinear equations.

III. Location of Minimum Pressure in Laterals Running Downhill

• The location of minimum pressure in a lateral running downhill is where the slope of

the friction loss curve, J, equals the ground slope.

73

• The above assertion is analogous to a pre-calculus "max-min problem", where you take

the derivative of a function and set it equal to zero (zero slope).

Here we are doing the same thing, but the slope is not necessarily zero.

Hazen-Williams Equation

87.4852.1

12(10)1.217J

D

C

Q(5.14)

for J in meters of friction head loss per 100 m (or ft/100 ft); Q in lps; and D in mm

In this equation we will let

xS

qQQ

e

a

1 (5.15)

for multiple, equally-spaced sprinkler outlets spaced at Se (m) from each other, with

constant discharge of qa (lps). Ql is the flow rate at the lateral inlet (entrance).

• To find the location of minimum pressure, let J = S, where S is the ground slope (in %,

because J is per 100 m), which is negative for downhill-sloping laterals.

Combining the two above equations and solving for x,

)])(()10(3[ 63.254.07 DSCQq

Sx I

a

e (5.16)

Where, x is the distance, in m, from the lateral inlet to the minimum pressure

• S is in percent; Se and x are in m; D is in mm; and Ql and qa are in lps.

• Note that the valid range of x is: 0 < x < L, and that you won't necessarily get J = S

over this range of x values:

• If you get x < 0 then the minimum pressure is at the inlet

• If you get x > L then the minimum pressure is at the end

• This means that the above equation for x is valid for all ground slopes: S = 0, S > 0

and S < 0

74

IV. Required Lateral Inlet Pressure Head

• Except for the most unusual circumstances (e.g. non-uniform downhill slope that

exactly matches the shape of the hf curve), the pressure will vary with distance in a

lateral pipe.

• According to Keller & Bliesner's design criterion, the required inlet pressure head to a

sprinkler lateral is that which makes the average pressure in the lateral pipe equal to

the required sprinkler pressure head, ha.

• We can force the average pressure to be equal to the desired sprinkler operating

pressure by defining the lateral inlet pressure head as:

Design Equation

hl = ha + 3/4hf +1/2Δhe (5.17)

• hl is the required pressure head at the lateral inlet.

• Strictly speaking, we should take approximately 0.4Δhe in the above equation, but we

are taking separate averages for the friction loss and elevation gradients.

• Of course, instead of head, h, in the above equation, pressure P could be used if

desired.

The value of Δhe is negative for laterals running downhill

75

For steep downhill slopes, where the minimum pressure would be at the lateral inlet,

it is best to let.

hf = -Δhe (5.18)

Thus, we would want to consume, or "burn up", excess pressure through friction loss

by using smaller pipes.

To achieve this equality for steep downhill slopes, it may be desirable to have more

than one pipe diameter in the lateral. A downhill slope can be considered "steep"

when (approximately)….

-Δhe > 0.3ha (5.19)

We now have an equation to calculate lateral inlet pressure based on ha, hf, and he.

However, for large values of hf there will be correspondingly large values of he. Thus,

for zero ground slope, to impose a limit on hf we will accept:

hf = 0.20 ha (for S = 0 only) (5.20)

• This is the same as saying that we will not allow pipes that are too small, that is, pipes

that would produce a large hf value.

An additional head term must be added to the equation for hl to account for the change in

elevation from the lateral pipe to the sprinkler (riser height):

refa hhhh 2

1

4

3h I (5.21)

or, in terms of pressure

refa PPPP 2

1

4

3PI (5.22)

V. Friction Losses in Pipes with Multiple Outlets

• Pipes with multiple outlets have decreasing flow rate with distance (in the direction of

flow), and this causes the friction loss to decrease by approximately the square of the

flow rate (for a constant pipe diameter).

• Sprinkler and trickle irrigation laterals fall into this hydraulic category.

• Multiply the head loss for a constant discharge pipe by a factor "F" to reduce the total

head loss for a lateral pipe with multiple, equally spaced outlets:

100

JFLh f (5.23)

Where F is from Eq. 8.9a as given below:

76

26

1

2

1

1

1

N

b

NbF

(5.24)

for equally spaced outlets, each with the same discharge, and going all the way to the

end of the pipe.

• All of the flow is assumed to leave through the outlets, with no "excess" spilled out

the downstream end of the pipe.

• N is the total number of equally spaced outlets.

• The value of b is the exponent on Q in the friction loss equation.

• The first sprinkler is assumed to be located a distance of Se from the lateral inlet

Eq. 8.9b (see below) gives F(α), which is the F factor for initial outlet spacings less than or

equal to Se.

)1(

)-(1-NF)F(

N

(5.25)

where 0 < α< 1

• Note that when α = 1, F(α) = F

• Many sprinkler systems have the first sprinkler at a distance of ½ Se from the lateral

inlet (α = 0.5), when laterals run in both orthogonal directions from the mainline.

VI. Lateral Pipe Sizing for a Single Pipe Size

• If the minimum pressure is at the end of the lateral, which is the case for no ground

slope, uphill and slight downhill slopes, then the change in pressure head over the

length of the lateral is:

Δ h = hf + Δ h e (5.26)

If we allow Δh = 0.20 ha, then

0.20ha = hf + Δhe (5.27)

0.20ha - Δhe = Ja FL/100 (5.28)

and,

FL

hhJ ea

a

20.0100 (5.29)

Where, Ja is the allowable friction loss gradient.

• Lateral pipe diameter can be selected such that J Ja

The above portion is the part of a standard lateral design criterion and will give a system CU

of approximately 0.97CU if lateral inlet pressures are the same for each lateral position, for

set sprinkler systems.

77

If the lateral is sloping downhill and the minimum pressure does not occur at the end of the

lateral, then we will attempt to consume the elevation gain in friction loss as follows,

ehfh (5.30)

FL

hJ e

a 100 (5.31)

Note that in this case Δh ≠ hf + Δhe. Rather, Δh = hmax - hmin, where:

1. hmax is either at the lateral inlet or at the end of the lateral, and

2. hmin is somewhere between the lateral inlet and the end

• Given a value of Ja, the inside diameter of the lateral pipe can be calculated from the

Hazen-Williams equation:205.0

852.1

a

)(J

KD

C

QI (5.32)

where Ql is the flow rate at the lateral inlet (Nqa) and K is the units coefficient in the

Hazen-Williams equation.

• The calculated value of D would normally be rounded up to the next available internal

pipe diameter.

VII. Lateral Design Example

VI.1. Given information:

L = 396 m (lateral length)

qa = 0.315 lps (nominal sprinkler discharge)

Se = 12 m (sprinkler spacing)

hr = 1.0 m (riser height)

slope = -2.53% (going downhill)

Pa = 320 kPa (design nozzle pressure)

pipe material = aluminum

VI.2. Calculations leading to allowable pressure head loss in the lateral:

Nn = 396/12 = 33 sprinklers F = 0.36

Ql = (0.315)(33) = 10.4 lps

Δhe = SL = (-0.0253)(396) = -10.0 m

(Pf)a = 0.20Pa - Δhe = 0.20(320 kPa) - 9.81(-10.0 m) = 162 kPa

(hf)a = 162/9.81 = 16.5 m

78

VI.3. Calculations leading to required lateral pipe inside diameter:

0.3Pa = 0.3(320 kPa) = 96.0 kPa

= 96.0/9.81 = 9.79 m

Now, 0.3ha < -Δhe (steep downhill). Therefore, may want to use hf = -Δhe. Then, Ja is:

m100 /m7.01)396)(36.0(

)0.10(100)

FL

Δh(100J e

a

m(5.33)

However, if 0.3ha > -Δhe, Ja would be calculated as:

mm/10011.6)(0.36)(396

(16.5)100

FL

Δh0.20h100J ea

a

(5.34)

For now, let's use Ja = 7.01 m/100 m. Then, the minimum pipe inside diameter is (C = 130 for

aluminum):

mm77.7)130

10.4(

7.01

1.21E12D

0.2051.852

(5.35)

which is equal to 3.06 inches.

In the USA, 3" aluminum sprinkler pipe has an ID of 2.9" (73.7 mm), so for this design it

would be necessary to round up to a 4" nominal pipe size (ID = 3.9", or 99.1 mm).

However, it would be a good idea to also try the 3" size and see how the lateral hydraulics

turn out (this is done below; note also that for Ja = 11.6, D = 70.0 mm).

VI.4. Check the design with the choices made thus far

The real friction loss will be:

mm/1002.14mm)(99.1130

10.41.21E12J 4.87-

1.852

(5.36)

mJFL

h f 06.3100

)396)(36.0)(14.2(

100 (5.37)

The required lateral inlet pressure head is:

hl = ha + 0.75hf + 0.5Δ he + hr (5.38)

hl = 320/9.81 + 0.75(3.06) + 0.5(-10.0) + 1.0 = 30.9 m

Thus, Pl is (30.9)(9.81) = 303 kPa, which is less than the specified Pa of 320 kPa, and this is

because the lateral is running downhill

79

VI.5. Calculate the pressure and head at the end of the lateral pipe

hend = hl - hf - Δ he = 30.9 - 3.06 - (-10.0) = 37.8 m (5.39)

which is equal to 371 kPa. Thus, the pressure at the end of the lateral pipe is greater than

the pressure at the inlet.

To determine the pressure at the last sprinkler head, subtract the riser height to get

37.8 m - 1.0 m = 36.8 m (361 kPa)

VI.6. Calculate the location of minimum pressure in the lateral pipe

))(()10(3q

Sx 63.254.07

a

e DSCQI (5.40)

m39.6)(99.1)2.53)(130(3(10)10.40.315

12x 2.630.547

The result is negative, indicating that minimum pressure is really at the entrance (inlet) to the

lateral pipe. The minimum sprinkler head pressure is equal to hl - hr = 30.9 - 1.0 = 29.9 m, or

293 kPa

VI.7. Calculate the percent pressure variation along the lateral pipe

The maximum pressure is at the last sprinkler (end of the lateral), and the minimum

pressure is at the first sprinkler (lateral inlet). The percent pressure variation is:

%21.0320

293361minmax

aP

PPP (5.41)

That is, 21% pressure variation at the sprinklers, along the lateral.

This is larger than the design value of 0.20, or 20% variation. But it is very close to

that design value, which is somewhat arbitrary anyway.

VI.8. Redo the calculations using a 3" lateral pipe instead of the 4" size

In this case, the location of the minimum pressure in the lateral pipe is

m196)(73.7)(130(2.53)3(10)10.40.315

12x 2.630.547 (5.42)

which is the distance from the upstream end of the lateral.

There are about 196/12 = 16 sprinklers from the lateral inlet to the location of

minimum pressure, and about 17 sprinklers from x to the end of the lateral.

80

Friction loss from x to the end of the lateral is:

87.4852.1

12end-x )7.73(

130

)(17)(0.3151.217(10)J

(5.43)

= 2.65 m/100 m

mh endxf 01.2100

)196396)(38.0)(65.2()(

(5.44)

Friction loss from the inlet to the end is;

87.4852.1

12 )7.73(130

4.10)10(217.1

endinletJ (5.45)

= 9.05 m /100 m

m12.9100

6)(396)(9.05)(0.3)(h endinletf (5.46)

Then, friction loss from inlet to x is:

(hf)inlet-x = 12.9 – 2.01 = 10.9 m (5.47)

The required lateral pipe inlet head is:

hl = ha + 0.75hf + 0.5Δhe + hr (5.48)

hl = 320/9.81 + 0.75(12.9) + 0.5(-10.0) +1.0 = 38.3 m

giving a Pi of (38.3)(9.81) = 376 kPa, which is higher than Pi for the 4” pipe

The minimum pressure head (at distance x = 196 m) is:

xinletexinletfIx )(Δ)(hhh h (5.49)

hx = 38.3 – 10.9 – (-0.0253)(196) = 32.4 m

giving a Px of (32.4)(9.81) = 318 kPa, which is very near Pa.

The pressure head at the end of the lateral pipe is:

hend = h - hf - Δ he = 38.3 - 12.9 + 10.0 = 35.4 m (5.50)

giving Pend of (35.4)(9.81) = 347 kPa, which is less than Pl. So, the maximum lateral pipe

pressure is at the inlet.

81

The percent variation in pressure at the sprinklers is based on Pmax = 376 -(1.0)(9.81) = 366

kPa, and Pmin = 318 - (1.0)(9.81) = 308 kPa:

0.18320

308366

P

PP%

a

minmax

P (5.51)

which turns out to be slightly less than the design value of 20% VI.9.

VI. What if the lateral ran uphill at 2.53% slope?

In this case, the maximum allowable head loss gradient is:

FL

Δh0.20h100J ea

a (5.52)

mm/1002.44)(0.36)(396

10.0-.81)0.20(320/9100

Which is negative because Δhe > 0.2ha, meaning that it is not possible to have only a 20%

variation in pressure along the lateral, that is, unless flow control nozzles and or other design

changes are made.

VI.10. Some observations about this design example

Either the 3" or 4" aluminum pipe size could be used for this lateral design. The 4"

pipe will cost more than the 3" pipe, but the required lateral inlet pressure is less with

the 4" pipe, giving lower pumping costs, assuming pumping is necessary.

Note that it was assumed that each sprinkler discharged 0.315 lps, when in reality the

discharge depends on the pressure at each sprinkler. To take into account the

variations in sprinkler discharge would require an iterative approach to the

mathematical solution (use a computer).

Most sprinkler laterals are laid on slopes less than 2.5%, in fact, most are on fields

with less than 1% slope.

82

Unit 6ECONOMIC PIPE SELECTION METHOD

I. Introduction

• The economic pipe selection method (Chapter 8 of the textbook) is used to balance

fixed (initial) costs for pipe with annual energy costs for pumping

• With larger pipe sizes the average flow velocity for a given discharge decreases,

causing a corresponding decrease in friction loss

• This reduces the head on the pump, and energy can be saved

• However, larger pipes cost more to purchase

Pipe Size (diameter)

Figure 6.1 Influence of pipe size on fixed energy and total costs for a given flow rate

• To balance these costs and find the minimum cost we will annualize the fixed costs,

compare with annual energy (pumping) costs

• We can also graph the results so that pipe diameters can be selected according to their

maximum flow rate

• We will take into account interest rates and inflation rates to make the comparison

• This is basically an "engineering economics" problem, specially adapted to the

selection of pipe sizes

• This method involves the following principal steps:

1. Determine the equivalent annual cost for purchasing each available pipe size

2. Determine the annual energy cost of pumping

3. Balance the annual costs for adjacent pipe sizes

83

4. Construct a graph of system flow rate versus section flow rate on a log-log scale

for adjacent pipe sizes

• We will use the method to calculate "cut-off" points between adjacent pipe sizes so

that we know which size is more economical for a particular flow rate

• We will use HP and kW units for power, where about % of a kW equals a HP

• Recall that a Watt (W) is defined as a joule/second, or a N-m per second

• Multiply W by elapsed time to obtain Newton-meters ("work", or "energy")

II. Economic Pipe Selection Method Calculations

1. Select a period of time over which comparisons will be made between fixed and annual

costs. This will be called the useful life of the system, n, in years.

• The "useful life" is a subjective value, subject to opinion and financial

amortization conditions

• This value could alternatively be specified in months, or other time period, but the

following calculations would have to be consistent with the choice

2. For several different pipe sizes, calculate the uniform annual cost of pipe per

unit length of pipe.

• A unit length of 100 (m or ft) is convenient because J is in m/100 m or ft/100 ft,

and you want a fair comparison (the actual pipe lengths from the supplier are

irrelevant for these calculations)

• You must use consistent units ($/100 ft or $/100 m) throughout the calculations,

otherwise the ΔJ values will be incorrect (see Step 11 below)• So, you need to know the cost per unit length for different pipe sizes

• PVC pipe is sometimes priced by weight of the plastic material (weight per unit

length depends on diameter and wall thickness)

• You also need to know the annual interest rate upon which to base the

calculations; this value will take into account the time value of money, whereby

you can make a fair comparison of the cost of a loan versus the cost of financing it

"up front" yourself

• In any case, we want an equivalent uniform annual cost of the pipe over the life of

the pipeline

• Convert fixed costs to equivalent uniform annual costs, UAC, by using the

"capital recovery factor", CRF

UAC = P (CRF) (6.1)

1i)(1

i)i(1CRF

n

n

(6.2)

84

where P is the cost per unit length of pipe; i is the annual interest rate (fraction);

and n is the number of years (useful life)

Of course, i could also be the monthly interest rate with n in months, etc.

• Make a table of UAC values for different pipe sizes, per unit length of pipe

• The CRF value is the same for all pipe sizes, but P will change depending on the

pipe size

• Now you have the equivalent annual cost for each of the different pipe sizes

3. Determine the number of operating (pumping) hours per year, Ot:

hrs/yearcapacity)(system

depth)annualsarea)(gros(irrigatedtO (6.3)

• Note that the maximum possible value of Ot is 8,760 hrs/year (for 365 days)

• Note also that the "gross depth" is annual, so if there is more than one growing

season per calendar year, you need to include the sum of the gross depths for each

season (or fraction thereof)

4. Determine the pumping plant efficiency:

• The total plant efficiency is the product of pump efficiency, Epump, and motor

efficiency, Emotor

Ep = EpumpEmotor (6.4)

• This is equal to the ratio of "water horsepower", WHP, to "brake

horsepower", BHP (Epump = WHP/BHP)

• Think of BHP as the power going into the pump through a spinning shaft, and

WHP is what you get out of the pump - since the pump is not 100% efficient in

energy conversion, WHP < BHP

• WHP and BHP are archaic and confusing terms, but are still in wide use

• Emotor will usually be 92% or higher (about 98% with newer motors and larger

capacity motors)

• Epump depends on the pump design and on the operating point (Q vs. TDH)

• WHP is defined as:

85

QH102

QHWHP (6.5)

where Q is in lps; H is in m of head; and WHP is in kilowatts (kW)

• If you use m in the above equation, UAC must be in $/100 m

• If you use ft in the above equation, UAC must be in $/100 ft

• Note that for fluid flow, "power" can be expressed as pgQH = yQH

• Observe that 1,000/g = 1,000/9.81 « 102, for the above units (other conversion

values cancel each other and only the 102 remains)

• The denominator changes from 102 to 3,960 for Q in gpm, H in ft, and

WHP in HP

5. Determine the present annual energy cost:

p

f

E

CtOE (6.6)

where Cf is the cost of "fuel"

• For electricity, the value of Cf is usually in dollars per kWh, and the value used in

the above equation may need to be an "average" based on potentially complex

billing schedules from the power company

• For example, in addition to the energy you actually consume in an electric motor,

you may have to pay a monthly fee for the installed capacity to delivery a certain

number of kW, plus an annual fee, plus different time-of-day rates, and others

• Fuels such as diesel can also be factored into these equations, but the power output

per liter of fuel must be estimated, and this depends partly on the engine and on

the maintenance of the engine

• The units of E are dollars per WHP per year, or dollars per kW per year; so it is a

marginal cost that depends on the number of kW actually required

6. Determine the marginal equipment cost:

• Note that Cf can include the "marginal" cost for the pump and power unit (usually

an electric motor)

• In other words, if a larger (higher head to overcome friction losses) pump & motor

cost more than a smaller pump & motor, then Cf should reflect that, so the full

cost of friction loss is considered

• If you have higher friction loss, you may have to pay more for energy to pump,

but you may also have to buy a larger pump and/or power unit (motor or engine)

• It sort of analogous to the Utah Power & Light monthly power charge, based

solely on the capacity to deliver a certain amount of power

Cf ($/kWh) = energy cost + marginal cost for a larger pump & motor (6.7)

OtCf

86

where "marginal" is the incremental unit cost of making a change in the size of a

component

• This is not really an "energy" cost per se, but it is something that can be taken into

account when balancing the fixed costs of the pipe (it falls under the operating

costs category, increasing for decreasing pipe costs)

• That is, maybe you can pay a little more for a larger pipe size and avoid the need

to buy a bigger pump, power unit and other equipment

• To calculate the marginal annual cost (MAC) of a pump & motor:

)kW(kWO

)$($CRFMAC

smallbigt

smallbig

(6.8)

where MAC has the same units as Cf; and $big -$small is the difference in pump +

motor + equipment costs for two different capacities

• The difference in fixed purchase price is annualized over the life of the system by

multiplying by the CRF, as previously calculated

• The difference in pump size is expressed as ABHP, where ABHP is the difference

in brake horsepower, expressed in kW

• To determine the appropriate pump size, base the smaller pump size on a low

friction system (or low pressure system)

• For BHP in kW:

pump

pumps

102E

HQBHP (6.9)

• Round the BHP up to the next larger available pump + motor + equipment size to

determine the size of the larger pump

• Then, the larger pump size is computed as the next larger available pump size as

compared to the smaller pump

• Finally, compute the MAC as shown above

• The total pump cost should include the total present cost for the pump, motor,

electrical switching equipment (if appropriate) and installation

• Cf is then computed by adding the cost per kWh for energy

• Note that this procedure to determine MAC is approximate because the marginal

costs for a larger pump + motor + equipment will depend on the magnitude of the

required power change

• Using $big -$small to determine MAC only takes into account two (possibly

adjacent) capacities; going beyond these will likely change the marginal rate

• However, this simple procedure provides a means to account for this potentially

real cost

• It also means you can have different values of E for each pair of adjacent pipe

sizes

87

7. Determine the equivalent annualized cost factor:

• This factor takes inflation into account:

1i)(1

i

ie

i)(1e)(1EAE

n

nn

(6.10)

where e is the annual inflation rate (fraction), i is the annual interest rate

(fraction), and n is in years

• Notice that for e = 0, EAE = unity (this makes sense)

• Notice also that Eq. 85 has a mathematical singularity for e = i (but, in practice, i

is usually greater than e)

8. Determine the equivalent annual energy cost:

E' = (EAE)(E) (6.11)• This is an adjustment on E for the expected inflation rate

• No one really knows how the inflation rate might change in the future

• But, how do you know when to change to a larger pipe size (based on a certain

sectional flow rate)?

Beginning with a smaller pipe size (e.g. selected based on maximum

velocity limits), you would change to a larger pipe size along a section of

pipeline if the difference in cost for the next larger pipe size is less than

the difference in energy (pumping) savings

• Recall that the velocity limit is usually taken to be about 5 fps, or 1.5 m/s

Determine the difference in WHP between adjacent pipe sizes by equating the annual plus

annualized fixed costs for two adjacent pipe sizes:

E’ (HPs1) + UACs1 = E’ (HPs2) + UACs2 (6.12)

's1s2

s2s1 E

)UAC(UACΔWHP

(6.13)

The subscript s1 is for the smaller of the two pipe sizes

The units of the numerator might be $/100 m per year; the units of the

denominator might be $/kW per year

This is the WHP (energy) savings needed to offset the annualized fixed cost

difference for purchasing two adjacent pipe sizes; it is the economic balance point

88

10. Determine the difference in friction loss gradient between adjacent pipe sizes:

s

s2s1s2-s1 Q

ΔWHP102ΔJ (6.14)

This is the head loss difference needed to balance fixed and annual costs

for the two adjacent pipe sizes

The coefficient 102 is for Qs in lps, and ΔWHP in kWYou can also put Qs in gpm, and ΔWHP in HP, then substitute 3,960 for102, and you will get exactly the same value for ΔJAs before, AJ is a head loss gradient, in head per 100 units of length (m

or ft, or any other unit)

Thus, ΔJ is a dimensionless "percentage": head, H, can be in m, and when you

define a unit length (e.g. 100 m), the H per unit meter becomes dimensionless

This is why you can calculate ΔJ using any consistent units and you will get thesame result

IV. Other Pipe Sizing Methods

• Other methods used to size pipes include the following:

1. Unit head loss method: the designer specifies a limit on the

allowable head loss per unit length of pipe

2. Maximum velocity method: the designer specifies a maximum average

velocity of flow in the pipe (about 5 to 7 ft/s, or 1.5 to 2.0 m/s)

3. Percent head loss method: the designer sets the maximum pressure variation

in a section of the pipe, similar to the 20%Pa rule for lateral pipe sizing

• It is often a good idea to apply more than one pipe selection method and compare the

results

• For example, don't accept a recommendation from the economic selection method if it

will give you a flow velocity of more than about 7 ft/s (2 m/s), otherwise you may

have water hammer problems during operation

• However, it is usually advisable to at least apply the economic selection method

unless the energy costs are very low

• In many cases, the same pipe sizes will be selected, even when applying different

methods

• For a given average velocity, V, in a circular pipe, and discharge, Q, the required

inside pipe diameter is:

πV4Q

D (6.15)

89

• The following tables show maximum flow rates for specified average velocity limits anddifferent pipe inside diameters (you can easily make tables like this in a spreadsheet

application)

Liters per Second

Velocity LimitD (mm) A (m2) 1.5 m/s 2 m/s10 0.00008 0.1 0.220 0.00031 0.5 0.625 0.00049 0.7 1.030 0.00071 1.1 1.440 0.00126 1.9 2.550 0.00196 2.9 3.975 0.00442 6.6 8.8100 0.00785 11.8 15.7120 0.01131 17.0 22.6150 0.01767 26.5 35.3200 0.03142 47.1 62.8250 0.04909 73.6 98.2300 0.07069 106 141400 0.12566 188 251500 0.19635 295 393600 0.28274 424 565700 0.38485 577 770800 0.50265 754 1,005900 0.63617 954 1,2721000 0.78540 1,178 1,5711100 0.95033 1,425 1,9011200 1.13097 1,696 2,2621300 1.32732 1,991 2,6551400 1.53938 2,309 3,0791500 1.76715 2,651 3,5341600 2.01062 3,016 4,0211700 2.26980 3,405 4,5401800 2.54469 3,817 5,0891900 2.83529 4,253 5,6712000 3.14159 4,712 6,2832100 3.46361 5,195 6,9272200 3.80133 5,702 7,6032300 4.15476 6,232 8,3102400 4.52389 6,786 9,0482500 4.90874 7,363 9,8172600 5.30929 7,964 10,6192700 5.72555 8,588 11,4512800 6.15752 9,236 12,3152900 6.60520 9,908 13,2103000 7.06858 10,603 14,1373100 7.54768 11,322 15,0953200 8.04248 12,064 16,0853300 8.55299 12,829 17,1063400 9.07920 13,619 18,158

D (inch) A (ft2) 5 fps 7 fps0.5 0.00136 3.1 4.3

0.75 0.00307 6.9 9.61 0.00545 12.2 17.1

1.25 0.00852 19.1 26.81.5 0.01227 27.5 38.6

2 0.02182 49.0 68.53 0.04909 110 1544 0.08727 196 2745 0.13635 306 4286 0.19635 441 6178 0.34907 783 1,097

10 0.54542 1,224 1,71412 0.78540 1,763 2,46815 1.22718 2,754 3,85618 1.76715 3,966 5,55220 2.18166 4,896 6,85525 3.40885 7,650 10,71130 4.90874 11,017 15,42340 8.72665 19,585 27,41950 13.63538 30,602 42,843

Cubic Feet per SecondVelocity Limit

D (ft) A (ft2) 5 fps 7 fps1 0.785 3.93 5.502 3.142 15.71 21.993 7.069 35.34 49.484 12.566 62.83 87.965 19.635 98.17 137.446 28.274 141.37 197.927 38.485 192.42 269.398 50.265 251.33 351.869 63.617 318.09 445.32

10 78.540 392.70 549.7811 95.033 475.17 665.2312 113.097 565.49 791.6813 132.732 663.66 929.1314 153.938 769.69 1,077.5715 176.715 883.57 1,237.0016 201.062 1,005.31 1,407.4317 226.980 1,134.90 1,588.8618 254.469 1,272.35 1,781.2819 283.529 1,417.64 1,984.7020 314.159 1,570.80 2,199.11

Gallons per Minute

90

Unit 7CENTER-PIVOT SPRINKLER IRRIGATION SYSTEM

I. Introduction and General Comments• Center pivots are used on about half of the sprinkler-irrigated lands in the USA.• Center pivots are also found in many other countries.• Typical lateral length is 1,320 ft (400 m), or ¼ mile.• The lateral is often about 10 ft above the ground.• Typically, 120-ft pipe span per tower (usual range: 90 to 250 ft), often with one-

horsepower electric motors (geared down).• At 120 ft per tower, a 1,320-ft lateral has about 11 towers; with 1-HP motors, that

comes to about 10 HP just for moving the pivot around in a circle.• The cost for a ¼ mile center pivot is typically about $45,000 (about $354/ac

or $875/ha), plus about $25,000 for a corner system.• For a ½ mile lateral, the cost may be about $75,000 (with out corner system).• In the state of Nebraska, there are said to be 50,000 installed center pivots, about 10 to

15% of which have corner systems.• The state of Texas has over 10,000 center pivots.• Center pivots are easily (and commonly) automated, and can have much lower labor

costs than periodic-move sprinkler systems.• Center pivot maintenance costs can be high because it is a large and fairly complex

machine, operating under "field" (sun, wind, dust, dirt) conditions.• The typical maximum complete rotation is 20 hrs or so, but some (120-acre pivots)

can go around in only about 6 hrs.• Running a pivot around at relatively high speeds makes the mechanical parts wear out

faster, and may also increase evaporation losses.• IPS 6" lateral pipe is common (about 6-5/8 inches OD); lateral pipe is generally 6 to 8

inches, but can be up to 10 inches for 2,640-ft laterals.• Long pivot laterals will usually have two different pipe sizes.• Typical lateral inflow rates are 45 - 65 lps (700 to 1,000 gpm).• At 55 lps with a 6-inch pipe, the entrance velocity is a bit high at 3 m/s.• Typical lateral operating pressures are 140 - 500 kPa (20 to 70 psi).• The end tower sets the rotation speed; micro switches and or cables keep other towers

aligned.

• Without a corner system or end gun (see below), /4 = 79% of the square area isirrigated. An end-gun will irrigate additional 5% of the total area. Whereas a cornerpivot can irrigate additional 12% of the total area. Thus total area irrigated comes out96% (79% + 5% + 12% = 96%) leaving rest of the area un-irrigated.

• For a 1,320-ft lateral (without an end gun), the irrigated area is 126 acres.• For design purposes, usually ignore soil WHC (WaZ); but, refill root zone at each

irrigation (even if daily).• Center pivots can operate on very undulating topography.• Some center pivots can be moved from field to field.• Below are some sample center pivot arrangements.

91

Figure 7.1 Showing the layout of the center-pivot systems

92

• Many farmers like extra capacity in the center pivot so they can shut off during windy times of theday, and still complete the irrigations in time.

• Some center-pivot irrigated fields have half the circle in one crop, and the other half in anothercrop (or fallow) - it can be difficult to make the pivot to stop at exactly the right position whensome sections of the circle are irrigated differently than others.

• Center pivots on rolling terrain usually have pressure regulators at each sprinkler; otherwise, thereis too much pressure variation among sprinklers, and the application uniformity is low.

• Some engineers claim that center pivots can have up to about 90% application efficiency.

A stationary sprinkle system applies water at constant rate, while the waterapplication rate at a point varies continuously with time during application by any movingsprinkle system. As the system approaches a point, the application rate starts from zero,increases to a maximum, and then decreases to zero again as the moving system passes overthe location. The water application under a center-pivot lateral is even more complicated. Theapplication rate varies along the lateral from a low value near the pivot to higher values at theouter end (Figure 2). This variation in the application rates is essential due to two reasons: i)area of the circular irrigated field increases with square of the radius, ii) time of waterapplication at a point decreases with increasing distance from the pivot as shown in the abovefigure. Thus instantaneous application rate patterns are different at different locations alongthe lateral. Since the application rate is the highest near the end of a center-pivot system andrunoff may occur at this location if it exceeds the soil intake rate.

Figure 7.2 Measured water application rates and application times along a center-pivot lateral.

Keller and Bliesner (1988) derived water-application rate profiles along differentpoints along the lateral of a center-pivot system as shown in Figure 8.8. The rate is maximumnear the end of the lateral and it decreases inward as explained earlier. Water application ratefor an elliptical profile is given by:

xjaj

xjaj

aj

eej I

T

IT

T

QdRI

4460/

(7.1)

93

Where,Ij = average application rate required at radial distance rj, mm/hr (in/hr)

d = gross depth of water required per irrigation, mm (in)

Taj = application time at radial distance rj, min

Ixj = peak application rate at radial distance rj, mm/hr (in/hr)

Qe = ratio of water effectively discharged through sprinklers to total system

discharge,

Re = effective portion of water discharged from sprinklers, most of which reachesthe soil-plant surface in decimal

Figure 7.3 Water application rates at different points along a center-pivot lateral(Source: Keller and Bliesner, 1990)

94

Thus average application rate is a function of the radial distance rj from the pivot and it is

proportional to the length of circular travel path at rj divided by the width of the application

profile. It is given by:

T

d.

wj

rπ2I pij

j (7.2)

Combining the above equations gives:

2eebj

j L

ORQK

wj

rπ2I (7.3)

Where

Ij = average application rate at radius rj, mm/hr (in/hr)

rj = radial distance from pivot to point under study, m (ft)

dpi = average peak gross infiltration required per day, mm (in.)

wj = width of stationary application patterns at rj, m (ft)

T = average daily operating time, hr

K = conversion constant 1146 for metric units 30.6 for English units)

L = radius of the irrigated field, m (ft)

Corner Systems

• Corner systems are expensive, and they don't irrigate the whole corner.

• Corner systems on center pivots have buried cables so that sprinklers in the corner

extension arm turn on and off individually (or in groups) as the arm swings out and then

back in again.

• The cables are buried about 5 ft (1.5 m) below the surface to prevent damage during

tillage operations (such as chiseling or "ripping").

• The end tower on the main part of the lateral has an antenna facing downward to detect

the signal from the buried cable, and to know when to begin to swing the extension arm

outward.

95

Figure 7.4 A view of center-pivot system with a corner system

• Usually, groups of sprinklers are controlled by separate valves in the extension arm

because the application rate and uniformity would differ too greatly from the desired

values if all the corner system sprinklers turned on (and off) simultaneously.

• There may be a control box at both the pivot point (center of field) and at the joint

where the extension arm connects to the main lateral; either box can be used to

program and control the pivot (e.g. to shut it down).

• Application uniformity in the corners is not as high as in the main circle area.

End Guns

Some pivots have an end gun that turns on in the corners, in which all other sprinklers

shut off via individual solenoid-actuated valves. The pivot stops in the corner while the end

gun runs for a few minutes. Others just slow down in the corners, turning on an end gun, but

leaving the other sprinklers running (at lower discharges); in these cases, a pressure

transducer might be used at the end of the lateral to indicate when the gun turns on (resulting

in a pressure drop), thus knowing when to slow the pivot. The figure below shows an

example of the approximate corner areas than might be irrigated by an end gun.

96

Figure 7.5 (a). Area irrigated by the main system and end gun.

The end-guns turn on when the lateral is in pointing toward a corner area (which is

when they should turn on) by angle measurements at the pivot point. In other cases, an

end gun on a center pivot lateral might be set to run all of the time (i.e. all the way

around the circle), effectively increasing the diameter of the irrigated area, but not

dealing with un-irrigated corner areas.

Figure 7.5 (b). Area irrigated by the main system and end gun.

97

Safety Switches

• Most center pivots have one or more safety switches.

• Some have switches to shut the whole machine off if any tower gets too far out of

alignment.

• Some also have safety switches to shut them off if the temperatures gets below

freezing (ice builds up and gets heavy, possibly collapsing the structure) - typically

shuts off at 32°F and turns back on at 40°F.

• With drop-down sprayer sprinklers, ice build-up is not so problematic.

• Some have safety switches connected to timers: if a tower has not moved in a

specified number of minutes, the system shuts down.

There may also be safety switches associated with the chemical injection equipment at the

lateral inlet location.

Figure 7.6 A view collapsed center pivot system

Drop Down Sprinkler

Almost all new center pivots have drop-down, low-pressure (20 - 25 psi) sprinklers.

Many older center pivots, which formerly had above-lateral impact sprinklers (50 - 60

psi) have been retrofitted with drop-down, low-pressure sprinklers. These features

help reduce energy (pumping) costs and reduce evaporation and wind drift.

Gooseneck tubes are used to convert older pivots to drop-down sprayers (sprinklers) -

they connect to the top of the center pivot lateral pipe at the same locations as the

previously-used impact sprinklers. New systems, designed for drop-down sprayers,

also use the gooseneck tubes because they help reduce the amount of sand and other

sediments, which might be in the lateral pipe, from moving through (and wearing out)

the sprinklers.

98

Center pivot laterals sometimes have manual flush valves (gate or butterfly) at the end

to periodically wash sediments out of the pipe. Some of the drop-down tubes are

polyethylene, others are PVC, and still others are galvanized steel.

The steel drop-down tubes have the advantage of rigidity and do not sway nearly as

much as polyethylene hoses (which usually have weights at bottom) under windy

conditions.

Figure 7.7 System with sprinkler heads below the lateral

II. System Capacity• The general center pivot design equation for system capacity is based on Eq.

5.4 from the textbook:

pa

fds TEk

kUR

fTk

dR

fT

AdKQ

1

2

1

2 ' (7.4)

Where, K is 2.78 for metric units and 453 for English units kl is (10,000 m2/ha)/(2.78 TI) =

1,145 for metric units kl is (43,560 ft2/acre)/(453 %) 30.6 for English units kf is the peak

period evaporation factor (Table 14.1) A is area (ha or acre) d is gross daily application depth

(mm or inch) d' is defined in the equation below (mm or inch) f is frequency in days per

irrigation.

T is operating time (hrs/day) R is the effective radius (m or ft) Ud is the peak-use ET rate of

the crop (mm/day or inch/day) Qs is the system capacity (lps or gpm).

99

• The gross application depth, d, is equal to dn/Epa, where Epa is the design application

efficiency, based on uniformity and percent area (pa) adequately irrigated.

• The operating time, T, is generally 20-22 hrs/day during the peak-use period.

• R is the effective radius, based on the wetted area from the center pivot.

• The effective radius is about 400 m for many center pivots.

• R « L + 0.4w, where L is the physical length of the lateral pipe, and w is the wetted

diameter of the end sprinkler.

• This assumes that approximately 0.8 of the sprinkler radius beyond the lateral pipe is

effective for crop production.

• Note that, for center pivots, Qs is proportional to Ud, and d and f are generally not

used, which is similar to drip irrigation design.

• Usually, for center pivot design, f = 1 day. So, if you use f > 1 day, you must also

increase d or d' to accommodate f number of days.

III. Gross Application Depth

If a center pivot is operated such that the water holding capacity of the soil is

essentially ignored, and water is applied frequently enough to satisfy peak-

use crop water requirements, then use dn/f = Ud, and

eepa

df

pa

dfs ORDE

Uk

E

Ukd ' (7.5)

where d' is the gross daily application depth (mm/day or inches/day); and kf is a peak-

use period evaporation factor, which accounts for increased soil and foliage

evaporation due to high frequency (daily) irrigation.

When LR > 0.1, the LR can be factored into the equation as:

pa

df

eepa

df

ELR

Uk

ORDELR

Ukd

)1(

9.0

)1(

9.0'

(7.6)

Which is the same as Eq. 14.1b from the textbook, except that DEpa, Re and Oe are all

as fractions (not percent).

Values of kf can be selected for the peak period from Table 14.1 of the textbook for

varying values of frequency, f.

Values for non-peak periods can be computed as described in the textbook on page

314:

0.1/)100(

'/)'100()1(k '

f

PTPT

PTPTk f (7.7)

100

Where, kf and PT are for the peak-use period (Table 14.1), and k'f and PT are the

frequency coefficient and transpiration percentage (PT) for the non-peak period.

ET

TPT (7.8)

• PT and PT' can be thought of as the basal crop coefficient (Kcb), or perhaps

Kcb - 0.1 (relative to alfalfa, as per the note in Table 14.1).

• It represents the transpiration of the crop relative to an alfalfa reference.

IV. Water Application along the Pivot Lateral• A major design difficulty with a center pivot is maintaining the application rate

so that it is less than the intake rate of the soil.

• This is especially critical near the end of the lateral where application rates

are the highest.

• As one moves along the center pivot lateral, the area irrigated by each unit length of

the lateral (each 1 ft or 1 m of length) at distance r from the pivot point can be

calculated as:

rrra 2)5.0()5.0( 22 (7.9)

This is equal to the circumference at the radial distance r.

• The portion of Qs (called q) which is applied to the unit strip at distance r is:

22

22

R

r

R

r

A

a

Q

q

s

(7.10)

2

2

R

rQq s (7.11)

where q can be in units of lps per m, or gpm per ft

This gives the amount of water which should be discharging from a specific unit

length of lateral at a radial distance r from the pivot point.

The q value at the end of the lateral (r = R) per ft or m is:

Use q to select the nozzle size, where qnozzle = q Se

101

UNIFORMITY OF A CENTER PIVOT

I. Introduction• The calculation of an application uniformity term must take into account the irrigated

area represented by each catch container.

• It is more important to have better application uniformity further from the pivot point

than nearer, because the catch containers at larger distances represent larger irrigated

areas.

• If the catch containers are equally spaced in the radial direction, the area represented

by each is directly proportional to the radial distance.

II. Equation for Center Pivot CU

• The equation for CU proposed by Heermann and Hein is (ASAE/ANSI S436):

(7.12)

Where, CU is the coefficient of uniformity; di is the depth from an individual container; ri

is the radial distance from the pivot point; and, n is the number of containers.

• First calculate the summations

)(11 ii

nn

irdiand

(7.13)

• Then, perform the outer summation to determine the CU value.

• That is, don't recalculate the inner summation values for every iteration of the outer

summation - it isn't necessary.

• It is usually considered that a center pivot CU should be greater than 85%.

• Note that nobody ever puts a whole grid of catch cans in a center pivot field.

• If the radial distances, n, are equal, the sequence number of the can (increasing with

increasing radius) can be used instead of the actual distance for the purpose of

calculating application uniformity.

Consider the following two figures:

102

Figure 7.8 Illustration of data collection for evaluating the system

103

III. Standard Uniformity Values

You can also calculate the "standard" CU or DU if you weight each catch value by

multiplying it by the corresponding radial distance.

To obtain the low ¼ , rank the un-weighted catches, then start summing radii

(beginning with the radius for the lowest catch value) until the cumulative value is

approximately equal to ¼ of the total cumulative radius.

This may or may not be equal to ¼ of the total catch values, because each catch

represents a different annular area of the field.

Finally, divide the sum of the catches times the radii for this approximately ¼ area by

the cumulative radius.

This gives the average catch of the low ¼...

Don't rank the weighted catches (depth x radius) because you will

mostly get the values from the low r values (unless the inner catches are

relatively high for some reason), and your answer will be wrong.

Don't calculate the average of the low ¼ like this. (because the lowest ¼

of the catches generally represents something different than ¼ of the

irrigated area):

Actually, the equation at the right is all right, except for the value "n/4", which is

probably the wrong number of ranked values to use in representing the low ¼.

You can set up a table like this in a spreadsheet application.

Ranked Center Pivot Catches

Radius, r Cumulativer

Depth, d d*r Cumulatived*r

smallest

largest

Totals: — —

• Note that when you rank the depths, the radius values should stay with the same depth

values (so that the radius values will now be "unranked"; all mixed up).

• To get the average weighted depth for the whole pivot area, divide the total "Cumulative

d*r" by the total "Cumulative r" (column 5 divided by column 2).

104

• Find the row corresponding closest to ¼ of the total "Cumulative r" value, and

take the same ratio as before to get the weighted average of the low % area.

• Look at the example data analysis below:

Radius,

r

Cum. r Depth,

d

d*r Cum.

d*r

120 120 0.52 62.6 62.6

900 1,020 0.95 851.9 915

160 1,180 1.29 205.8 1,120

340 1,520 1.31 445.6 1,566

1000 2,520 1.46 1,456.

3

3,022

1040 3,560 1.46 1,514.

6

4,537

240 3,800 1,48 355.3 4,892

800 4,600 1.50 1,203.

9

6,096

860 5,460 1.53 1,315.

0

7,411

480 5,940 1.58 757.3 8,168

1280 7,220 1.58 2,019.

4

10,188

980 8,200 1.60 1,569.

9

11,758

540 8,740 1.63 878.2 12,636

360 9,100 1.65 594,2 13,230

460 9,560 1.67 770.4 14,000

880 W.440 1.70 1,495.

1

15,496

320 10,760 1.72 551.5 16,047

1140 11,900 1.75 1,992.

2

18,039

1160 13,060 1.75 2.027

2

20,067

280 13,340 1.82 509.7 20,576

720 14,060 1.82 1,310.

7

21,887

1300 15,360 1.82 2,366.

5

24,253

200 15,560 1.84 368.9 24,622

420 15,980 1.84 774.8 25,397

440 16,420 1.89 833.0 26,230

1020 17,440 1.89 1,931. 28,161

105

Notice that the depth values (3rd column) are ranked from low to high.

Notice that the maximum value of cumulative r is 44,220 & maximum cumulative d*r

is 87,784. Then, the weighted average depth for the entire center pivot is equal to

87,784/44,220 = 1.985 (whatever units).

One quarter of 44,220 is equal to 11,055 which corresponds most closely the row in

the table with depth = 1.72. For the same row, divide the two cumulative columns (Col

5/Col 2) to get 16,047/10,760 = 1.491, which is approximately the average of the low

¼.

Finally, estimate the distribution uniformity for this data set as:

%75985.1

491.1100

DU (7.14)

Note that in this example, the average of the low ¼ was, in fact, based on approximately the

first n/4 ranked values.

Consider the weighed catch-can data plotted below:

Figure 7.9 Accumulative water application depth along the lateral

• As in any application uniformity evaluation, there is no "right" answer. The results are

useful in a comparative sense with evaluations of other center pivots and other on-farm

irrigation systems.

• However, a plot of the catches can give indications of localized problems along the

center pivot radius.

106

IV. The Field Work• It may take a long time for the full catch in containers near the pivot point, and

because these represent relatively small areas compared to the total irrigated area, it is

usually acceptable to ignore the inside 10% or 20% of the radius.

• The pivot quickly passes the outer cans, but takes longer to completely pass the inner

cans, so you can collect the data from the outer cans sooner.

• The pivot should not be moving so fast that the application depth is less than about 15

mm.

• Catch containers can be placed beyond the physical length of the lateral pipe, but if

they are so far out that the catches are very low, these can be omitted from the

uniformity calculations.

• Catch containers should be spaced in the radial direction no further than about 30% of

the average wetted diameter of the sprinklers.

• There is often an access road leading to the pivot point for inspection, manual

operation, maintenance, and other reasons.

• If the crop is dense and fairly tall (e.g. wheat or maize) it will be difficult to perform

the evaluation unless the cans are placed on the access road.

• Otherwise, you can wait until the crop is harvested, or do the test when the crop is still

small.

• Some people recommend two radial rows of catch cans, or even two parallel rows, to

help smooth out the effects of the non-continuous movement of towers (they start and

stop frequently to keep the pivot lateral in alignment).

• Some have used troughs instead of catch cans to help ameliorate this problem.

• Note that if the field is sloping or undulating, the results from one radial row of catch

cans may be quite different from those of a row on another part of the irrigated circle

• See Merriam and Keller (1978).

LINEAR MOVE SYSTEMSI. Introduction

• Mechanically, a linear move system is essentially the same as a center pivot lateral, but

it moves sideways along a rectangular field, perpendicular to the alignment of the

lateral pipe

• The variation of flow rate in a linear move lateral is directly proportional to distance

along the lateral pipe, whereas with center pivots it is proportional to a function of the

square of the distance from the pivot point.

• A center or end tower sets the forward speed of the machine, and the other towers just

move to keep in line with the guide tower (this is like the far end tower on a center

pivot).

• Usually, each tower is independently guided by cables and micro-switches as for a

center pivot - this keeps the lateral pipe in a straight line (aligned with itself).

107

• Alignment with the field is usually not mechanically "enforced", but it is "monitored"

through switches in contact with a straight cable along the center of the field, or along

one end of the field.

• The center tower has two "fingers", one on each side of the cable; usually slightly

offset in the direction of travel (they aren't side by side). The fingers should be in

constant contact with the cable - if one is lifted too far a switch will be tripped,

shutting the system down (because the whole lateral is probably getting out of

alignment with the field).

• If the cable is broken for any reason, this should also shut the system down because

the fingers will lose physical contact.

• If the lateral gets out of alignment with the field and shuts off, it will be necessary to

back up one side and or move the other side forward until it is in the correct position.

• This can involve electrical "jumps" between contacts in the control box, but some

manufacturers and some installers put manual switches in just for this purpose.

• Some linear moves are fitted with spray nozzles on drop tubes or booms.

• If they are spaced closely along the lateral, it may be necessary to put booms out

beyond the wheels at tower locations, either in back of the lateral or on both sides of

the lateral.

Water Supply• Water is usually supplied to the lateral via:

1. a concrete-lined trapezoidal-sectioned ditch, or

2. a flexible hose (often 150 m in length), or

3. automatic hydrant coupling devices with buried mainline

• Hose-fed systems require periodic manual reconnection to hydrants on a mainline - it is

kind of like a periodic move system, and you have to ask yourself whether the Wnear

move machine is worth the cost in this case.

• With the automatic hydrant coupling machines (see Fig. 15.3) there are two arms with

pipes and an elbow joint that bends as the Wnear move travels down the field. The two

arms alternate in connecting to hydrants so as neither to disrupt the irrigation nor the

forward movement of the machine. These are mechanically complex.

• The advantage of hose-fed and automate coupling Wnear moves is that you don't need

to have a small, uniform slope in the direction of travel because water is supplied from a

pressurized mainline instead of an open channel.

• On ditch-fed systems there can be a structure at the end of the field that a switch on the

linear move contacts, shutting down the pump and reversing the direction of movement so

that it automatically returns to the starting end of the field.

• The advantages and disadvantages of the ditch-feed system are:

108

Pros

• Low pressure (energy) requirement

• Totally automated system

• More frequent irrigations than hose-fed, since no one needs to be available to

move the hose

Cons

• Trash and seeds and sediment pass through screen and may plug nozzles.

• The pump must be on (move with) the lateral, causing extra weight.

• Should have uniform slope along the lateral route.

Pros and Cons Compared to a Center Pivot

Pros

• Easy irrigation of a rectangular field (important if land is expensive, but not

important if land is cheap and water is scarce).

• Application rate is uniform over length of lateral, rather than twice the average

value at the end of the center pivot.

• No end gun is required.

Cons

• The lateral does not end up right back at the starting point immediately after

having traversed the irrigated area – you either have to “deadhead” back or irrigate inboth directions.

May be more expensive than a pivot due to extra controls, pump on ditch feed, or

more friction loss in the flexible feed hose (the hose is fairly expensive).

109

110

111

112

113

114

Unit 8TRICKLE IRRIGATION

INTRODUCTIONTrickle irrigation is a relatively new irrigation method developed in middle of the

twentieth century. In this method water is applied slowly through tiny openings called

emitters or applicators located on water delivery lines near the plants. Most emitters are

placed on the ground surface, but these can be buried as well. One or more emitters are used

to apply water to a plant depending upon water requirement of the plant and some other

factors which will be discussed later in this Chapter. This method is extremely useful in water

scarcity areas. Micro irrigation and localized irrigation are other names often used for trickle

irrigation. Trickle irrigation is further classified as drip, spray, bubbles, and hose-basin

irrigation techniques depending upon the type of emitter used to apply water as discussed in

the next section. Some writers use the words 'trickle' and 'drip' synonymously which is

technically not correct as drip is one type of trickle (Keller and Blissner, 1990).

ADVANTAGESTrickle irrigation has become popular in water scarcity areas due to its high

efficiency. Efficiency of this system may be 90 percent or more if properly designed,

managed and operated. Some of the main advantages of this method are:

i) Water Saving: High efficiency of the system and partial wetting of the soil surface

result in much saving of irrigation water. Furthermore water savings are also achieved by

light water application to young plantings and young orchards because with conventional

methods heavy irrigations result in more wastage. Surface water runoff and deep percolation

are also avoided or reduced in trickle irrigation. Small stream flows can be more conveniently

used with this system.

ii) Control of Weed Growth: Weed growth is minimized due to limited soil surface

wetting. Field operations are also less interrupted due to partial surface wetting.

iii) Fertilizer Application: Dissolved fertilizers and other chemicals can be applied more

effectively as they are applied near the plants. This will also save additional cost of fertilizer

application. The fertilizers may be injected by venturi or injection pump (positive

displacement) which may be electric or water driven.

iv) Labour Saving: This system can be easily automated which will result in saving of

irrigation labour.

115

v) Saline Water: Irrigations are applied frequently at high moisture content that keeps

the soil solution more dilute. Due to this more salty water can be used by this method as

compared to other irrigation methods.

vi) Levelling: A field with rolling topography can be easily irrigated with trickle

irrigation, thus saving cost of land levelling.

vii) Crop Yield: The plants are not subjected to water stress due to frequent water

application. This may enhance plant growth and crop yield.

DISADVANTAGESHigh Initial Cost: Like sprinkler system, initial cost of trickle system is also high.

Therefore use of trickle irrigation is suitable for high value cash crops, vegetables and

orchards.

Clogging: Filtered water is essential to avoid clogging. Emitters are subjected to clogging

by mineral particles and organic matter, present in irrigation water. Such particles must be

removed by filtration before water enters the pipe networks. Water may be drained from the

pipes or it should be chemically treated to avoid clogging by algae and rust.

Salt Accumulation: Salt accumulated on the soil surface and around the wetted perimeter

may become injurious if use of saline water is prolonged. Light rain shower may leach down

these salts into active root zone under such condition, irrigation should be applied as planned

to dilute and leach any salts out of the root zone.

TYPES OF TRICKLE IRRIGATIONDrip Irrigation: In this method, water is applied slowly like drops by single or multi outlet

emitters. The emitters may be spaced apart in case of point emitters whereas they are more

closely spaced for line source emitters. Due to small opening of the emitters, special care

should be taken to avoid clogging.

Bubbler Irrigation: In bubbler irrigation water is applied through small diameter tube (less

than 10 mm) which is connected to the lateral line to basin of individual tree. Application rate

may be varied by varying diameter or length of the bubbler tube. Higher discharge of this

system may cause surface runoff and deep percolation.

Spray Irrigation: Spray irrigation resemble micro-sprinklers in which small sprinklers are

used to spray as a mist on the soil surface. This system may be designed to wet all or part of

the soil surface. Discharge rate is usually less than 2 lpm. In this system evaporation and drift

losses are more than the other type of trickle systems.

Subsurface Irrigation: In subsurface irrigation the emitters of a drip system are placed

below the land surface. The subsurface irrigation is different than sub-irrigation in which

water table is raised by blocking outlet of tile drainage system or by some other arrangement.

116

COMPONENTS OF A TRICKLE IRRIGATION SYSTEMBasic components of a typical trickle irrigation system consists of pump, control head,

main and sub-main lines, lateral lines, emitters, fittings, valves, pressure and flow measuring

devices. Main components of a typical trickle system are shown in Fig. 8.1. The main line is

connected to the water supply source and it supply water to the manifolds (sub-mains) and

laterals. The manifold is the part of pipe network between the main line and laterals. It is

normally burried but can be laid on surface as well. Lateral lines are 10 to 25 mm diameter

polyethylene or PVC hose or tubing and they supply water to the emitters.

Control Head: The components of control head comprise filters, chemical injection, tank

and injector flow measuring and pressure regulating devices. Good filtration is essential to

avoid clogging of emitters which causes poor water distribution. Screen and graded gravel-

sand filters and settling basins are commonly used for filtering and keeping contamination

out of the system. Positive displacement pump with piston-type injector or a venturi device

are commonly used to inject liquid fertilizers and other chemicals (insecticides acids,

algacides, etc) in irrigation in the trickle irrigation system.

Figure 8.1 Primary components of a trickle irrigation system.

Main and Sub-main pipelines: Filtered water is supplied through the main pipeline to the

sub-mains (manifold), which serves a group of laterals. For trickle irrigation, the operating

pressure is lower as compared to sprinkler; therefore relatively cheaper pipe can be used.

Normally these pipes are of polyvinyl-chloride (PVC) and sometime asbestos-cement pipe is

used for the main line. The sub-main is of polyethylene or PVC with 20 to 80 mm diameter.

117

There should be values on the mainline and sub-main to regulate the flow and for periodic

flushing.

Lateral Lines: The lateral lines are usually connected to the sub-main but in some cases

directly to the main line. The lateral lines are made of black polyethylene (PE) plastic ranging

in diameter from 8 to 25 mm. For good uniformity, pressure variation in a lateral line should

not exceed 10 percent.

Valves: Different types of valves are used for proper operation and management of a trickle

irrigation system. Manifold valves control water supply from the main pipeline to the

manifolds. Lateral or header valves are located on the manifold risers that supply water to

each lateral or header. Flush-out valves are attached at the ends of main lines, manifolds, and

laterals to flush the pipe network periodically.

Emitters: Emitters are water applicator devices used in different types of trickle systems.

They are designed to dissipate pressure and to discharge a small uniform flow at a constant

rate. Ideal emitters should have a constant flow over some variation of pressure and also

some means of flushing to reduce clogging. Types of emitters include long-path emitters,

orifice emitters, vortex emitter and flushing emitters. The later emitters are further of

continuous-flushing type if they permit continuous passage of large solid particles while

operating or compensating emitters which have constant discharge over wide range of

operating pressure. In addition to the single outlet emitters, the multi-outlet emitters supply

water to two or more points through auxiliary tubing.

Point-Source and Line-Source Applications: When emitters are widely spaced on the

lateral tubing, wetting pattern of an individual emitter is of elliptical shape as shown in Fig.8.2.

Figure 8.2 Wetting profiles for equal volumes (12 gal) of water applied at three different applicationrates on on a dry soil (Source: Keller and Bliesner, 1990, p.458)

60 45 30 15 15 30 45 60

Width, cm

Legendo 1gph for 12 h

2ٱ gph for 6 hΔ 4 gph for 13 h

Emitter

1530

4560

118

This is called point-source application and emitters are spaced 1 m or more. In line-source

application, the emitters are closely spaced at intervals of about 0.6 m on small diameter hose

(less than 25 mm). The line-source tubing may be single chamber tubing or double-chamber

tubing. In double chamber tubing larger holes at longer intervals are made in the inner wall

while smaller diameter orifices are punched at 0.15 to 0.6 m in the outer wall. Porous-wall

hose has small holes uniformly spaced through which water oozes under pressure.

There is a lateral for each row of crops or plants. But for some horticultural crops, one

line may serve two crop rows. On the other hand two lateral lines may be need for each plant

row if emitter flow is small and water need of plants is high. Special layout of emission

points such as zigzag, pigtail or multi-outlet emitters are used for widely-spaced trees as

shown in Fig. 8.3.

Small water application devices used to spray or mist water are called sprayers. They

discharge a uniform spray of water to cover an area of 1 to 10 m2.

System Layout: The pipe network layout of a trickle system should be in such a way as to

deliver water to the emitters at the designed pressure. The system should be designed such

that a part of it can be operated at a time if so required. On level field with mild slope, the

manifold is placed in middle of the field in order to place the laterals on both side of the

manifold as shown in Fig. 8.4. If the slope is high, move the manifold uphill in order to offset

the excessive pressure drop. Gain in pressure due to elevation difference will allow to use

longer lateral on the down hill side of the manifold as shown in Fig. 8.5.

Emission Uniformity: Distribution of water in a trickle irrigation system is measured by

emission uniformity, EU which can be calculated from field data as:

EU = 100 qn/qa (8.1)

Where

qn = average discharge of the lowest one-fourth of the data set (emitter discharges),

L/h (gph)

qa = average discharge rate of all the emitters measured in the field, L/h (gph)

A system with EU greater than 90% is excellent, between 90 to 80% good, 80 to 70% fair

while less than 70% is considered poor (Merriam and Keller, 1978, page 137).

Wetted area

119

Figure. 8.3 Various Emission Point Layouts for Wide-spread Tree Plants.(Source: Keller and Bliesner, 1990, page 436).

Sp

Sp

Tree

SeWetted area

Lateral widthEmitters

W

Shaded area

S rS 1

= S r

A. Single lateral for each row of trees (3 emitters/tree, Pw = 30%)

Area perTree

WettedAreaS r

B. Double laterals for eachTree row (Pw ≡ 60%)

C. Zigzag lateral for eachTree row.

Emitter

EstimationPointsD. Pigtail with 4

emittersPer tree. (Pw ≡ 40%)

F. Multiexit 6 outlet emitterwith distributuin tubing(Pw ≡ 60%)

Sp

120

Figure 8.4 A typical layout for Trickle Irrigation System.

Figure 8.5 A subunit with manifold placed uphill from middle of the field.

I

II

Subunit

Subunit

Subunit IV

Subunit III

Manifold

Control Valve

Water supply &Control valves

Lateral

Emitter

Pressure regulator

Header

Laterals

Connection withmainline

Slop

e

Slope

121

Wetted Area: Trickle irrigation does not wet the whole soil surface. Only the soil surface

near the emitter is wetted which depends on rate and volume of the emitters, slope and soil

characteristics. The wetted area on the soil surface is usually small and it is maximum at 15 to

30 cm depth beneath the emitters. The wetted area, Pw is defined as the average wetted area at

15 to 30 cm depth divided by the total surface area of the field. The wetted area of a trickle

irrigation system is usually between 30 to 70 percent. Apart from other factors, the wetted

area also depends on rainfall, type of crop and plants grown. Higher rainfall will give better

crop production for same wetted area and vice versa.

Estimating Wetted Area: The wetted area is the average horizontal area wetted in top 15 to

30 cm as explained earlier. The wetted area can be computed from the following equation for

straight single line lateral (Keller and Bliesner, 1990):

100100/

Pw

drp

eP

PSS

wSN

(8.2)

Where, Pw = percentage of land wetted along a horizontal strip 15 to 30 cm below the land

surface, Np = number of emitters per tree, w is wetted width in m, Sp = is the distance

between plants in the row, m, and Sr = is the distance between plant rows, m.

The above equation is valid if Se Se where Se is the optimal emitter spacing,

which is normally 80% of the wetted diameter. If Se > Se-, then replace Se in the above

equation by S.For double-lateral system and other layouts shown in Fig. 8.3, the lateral should be laid Seapart to maximize the wetted area which can be estimated as:

100100/

2/)(NP

'e

w

drp

ee

PSS

wSS(8.3)

Example 8.1: Tree spacing in a garden is 3 m with 5 m row to row distance and 3 emitters

per tree. Discharge of emitter is 4 litres/hr. Calculate wetted area for a) A single row of

emitters & b) Zigzag layout as shown in Fig. 8.3C. Measurement shows wetted width is 1.5

m and Se = 1.2 m.

a) Using equation for single lateral, Np = 3

36%10053

1.51.23Pw

122

b) For the zigzag layout, Np = 4

62.4%10053

2/)5.12.1(1.24Pw

WATER REQUIREMENTSCrop water requirements for trickle irrigation are different than the convential crop

water needs due to partial wetting of the soil surface. Under trickle irrigation evaporation

from soil surface is less due to its partial wetting. Water use under trickle irrigation mostly

depends on transpiration due to minimum soil evaporation. Transpiration under trickle

irrigation can be estimated as (Keller and Bliesner, 1990):

Td = Ud [0.1 (Pd)0.5] (8.4)

Where Td = average daily transpiration rate during the peak use month for a particular crop

under trickle irrigation, mm/day, Ud = Conventially estimated average daily water

requirements during the peak use month for a mature crop, mm/day, and Pd = percentage of

soil surface area shaded by the crop at midday in percent. This can be estimated by inspection

at noon and it may vary from some low value to a maximum of 80% of mature orchard.

Seasonal transpiration can be estimated by replacing Ud with the total estimated

seasonal consumptive use as:

Ts = U [0.1(Pd)0.5] (8.5)

Where Ts = seasonal transpiration under trickle irrigation, mm and U = conventially

estimated seasonal consumptive use for the mature crop, mm.

Seasonal Water RequirementNatural rainfall fulfils some of crop water needs therefore net irrigation requirement

should be decreased accordingly. Thus net seasonal irrigation depth, Dn is given by:

Dn = (U – Re – Mi) [0.1 (Pd)0.5] (8.6)

Where Re = effective precipitation during the growing season, mm and Ms = initial soil

moisture stored in the root zone, mm if any

Depth per Irrigation: Trickle irrigation usually wets the soil surface partially. Therefore,

irrigation depth is calculated as:

ZPw

ax W100100

MADd (8.7)

123

Where dx = maximum net depth of water to be applied per irrigation, mm, MAD =

management allowed deficit in percent, Wa = available water holding capacity of the soil,

mm and Z = plant root depth, mm.

Net water depth can be calculated as:

dn = Td f (8.8)

Where dn = net water depth applied per irrigation to meet crop water needs, mm, f = actual

irrigation interval (frequency), days, and Td = average daily transpiration during peak-use

period, mm.

Leaching Requirement: Salinity may develop if saline water is used for longer time in arid

and semi-arid regions where rainfall is insufficient to wash salts below the root zone. Under

such condition, additional water is applied to leach salts out of the active root zone. However,

it is not essential to apply extra water for leaching with each of irrigation. The following

equation may be used to estimate leaching requirement.

dw

iw

Nn

N

nn

n

EC

EC

LD

L

Ld

L

)()(LR t (8.9)

Where

LRt = leaching requirement ratio under trickle irrigation,

dn = net depth of application per irrigation to meet consumptive use requirements,

mm

Dn = net annual or seasonal irrigation depth to meet consumptive use requirements,

mm

Ln = net leaching requirement for each irrigation, mm

LN = net annual leaching requirement, mm

ECw = electrical conductivity of the irrigation water, dS/m (mmhos/cm), and

ECdw = electrical conductivity of the drainage (deep percolation) water, dS/m.

Gross Irrigation Requirements: Gross irrigation depth and volume required can be

estimated from net water requirement, water required for leaching and irrigation efficiency of

the system. Irrigation efficiency in a trickle system mainly depends on application uniformity

(emission uniformity) if losses due to leaks, runoff and deep percolation are not much. The

application efficiency of low-quarter, Eq is the average of the lowest one-fourth volume

applied to the over all average of the measured data set. If losses are negligible then Eq is

equal to the measured EU.

Gross Depths and Volumes: Total or gross amount of water per irrigation, d may be

calculated knowing irrigation efficiency or emission uniformity. If leaching requirement is

small (LRt = 10%) then it may be neglected and irrigation depth is given by:

124

100/

dd n

EU

Tr (8.10)

or

100/

Td d

EU

Tr

On the other hand if LRt > 10% then

)0.1(

d100d n

tLREU (8.11)

tLREU )0.1(

T100d d

Where,

d = gross depth of application per irrigation, mm

d' = maximum gross daily irrigation requirement, mm

Tr = peak-use period transmission ratio

EU = emission uniformity, %

LRt = leaching requirement under trickle irrigation.

Gross volume of water required per day per plant is given by:

G = K d/f Sp Sr

Or

G = K d Sp Sr (8.12)

Where,

G = gross volume of water required per plant or per unit length of lateral per day, L/day

K = conversion constant which is 1.0 for metric units

Similarly gross seasonal volume of water can be estimated for TR > 1.0/(1.0- LRt) as:

100/

DV n

s EU

T

K

A r (8.13)

for TR 1.0/(1.0 – LRt)

)0.1(

D100V n

stLREUK

A

(8.14)

System Discharge: The total system discharge or capacity depends on the maximum number

of emitters operating at a given time. It can be calculated as:

125

rps

a

s SSN

qps

N

N

AKQ (8.15)

For uniformity spaced laterals that supply uniformly spaced emitters, the Qs is given by:

les

a

s SSN

q

N

AKQs (8.16)

Where,

Qs = Total system capacity, L/s

K = Conversion constant, 2.778 for metric units

A = Field area, ha, and

Ns = Number of operating stations

For line-source tubing where the discharge per unit length is given, replace qa/Se in the last

equation with discharge per meter of the lateral.

Operating Time: Operating time per season can be calculated as:

s

s

Q

VKOt (8.17)

Where, Ot = average operating time per season, hr, and K = conversion constant = 2.778 for

metric units.

Net Application Rate: The net application rate is the lowest application rate at which water

is applied to plants. It can be estimated as:

rp

a

SS

qK p

n

N

100

EUI (8.18)

Where,

In = net application rate, mm/h

K = conversion constant, 1.0 for metric units

Criteria for Emitter SelectionThe emitters are the most important and sensitive component of trickle irrigation.

Selection of the emitters mainly depends on the percentage of wetted area, reliability of the

emitter against clogging and malfunctioning, type of soil to be wetted, emitter discharge and

quality of irrigation water. Ideal emitters should be durable, cheap and give reliable

performance over wider range of pressure variation.

126

Emitter Discharge: Discharge or flow from an emitter or a sprayer can be expressed by an

empirical equation of the form:

Q = Kd Hx (8.19)

Where,

q = emitter flow rate, L/h (gph)

Kd = discharge coefficient

H = working pressure head at the emitter, m (ft)

x = emitter discharge exponent

The value of x characterizes discharge versus pressure relationship of an emitter. Higher the

value of x, more discharge will be affected by variations in pressure and vice versa (Fig. 8.6).

Figure 8.6 Discharge variation due to pressure changes for emitters having differentdischarge exponents (Source: Keller and Bliesner, 1990, page 430)

The exponent of long-path emitters is between 0.7 to 0.8 while tortuous path emitters have

values between 0.5-0.7. The orifice and nozzle type emitters and sprayers have the exponent

of 0.5. For fully compensating, x = 0.0 (Keller and Bliesner, 1990, p. 429).

The exponent x can be calculated knowing discharge at two different operating pressures as:

)/log(

)/(qlogx

21

21

HH

q (8.20)

Pressure head variation, %

Rated discharge

30

20

10

0

-10

-20

Dis

char

ge v

aria

tion

, %

-30 -20 -10 0 10 2030

x = 1.0

x = 0.75

x = 0.5x = 0.4

x = 0.0

Laminar, x = 1.0Long path, x = 0.75Orifice, x = 0.5Vortex, x = 0.4Fully compensating, x = 0.0

127

Where ql and q2 are measured emitter discharges at pressure head H1 and H2 respectively. Kd

can be calculated knowing the discharge exponent and using equation.

Sensitivity to Clogging: This is one of the major factors to be considered while selecting

emitters. Clogging mostly depends on size of the emitter openings and velocity of water

through the emitter. For low discharge, the size of the emitter should be between 0.25 to 2.5

mm but small diameter emitters are more sensitive to clogging and vice versa. Therefore to

avoid clogging, general recommendation is to remove all particles larger than one-tenth of the

diameter of emitter. Relatively larger opening and self-flushing emitters are less subjective to

clogging.

Coefficient of Variation: Discharge of emitters varies due to non-ideal operating and

manufacturing factors. The coefficient of variation is determined by measuring flow rate of

several identical emitters and it is computed as:

2/1

2/1321

v )1(

).......C

nq

nqqqqq

a

an (8.21)

Where

Cv = manufacturer's coefficient of variation

ql, q2,q3..qn discharge of individual emitters, l/h

qa = average emitter discharge (ql+ q2 +q3+ qn)/n, L/h, and

n = number of emitters tested.

The coefficient of variation for good point-source emitters should be less than 0.05. The

performance of the system would be unacceptable if Cv is higher than 0.15. For line-source

system, the above limits are doubled.

Temperature: Discharge of an emitter may be sensitive to water temperature due to

dependence of viscosity on temperature. As water flows through the pipes, its temperature

increases toward the ends of the laterals. Increase in discharge due to rise in temperature

partially offsets decrease in discharge due to pressure drop in long laterals. For different

emitter devices the change in discharge is about 1 percent for each 2 to 4°C. For more details,

the reader is referred to (Keller and Bliesner, 1990, page 495).

Evaluation and Design ConsiderationsIt is not possible to present here detailed design of trickle irrigation. For this the

reader is referred to an excellent and relatively latest text book by Keller and Bliesner (1990).

128

Evaluation: Evaluation of trickle irrigation system includes measuring different parameters

including discharge of emitters along selected laterals, emission uniformity, pressure

variation and efficiency factors. Discharge of emitters can be measured by collection, water

in a measuring flask or graduated cylinder. Pressure can be easily measured by pressure

gauge. Recommended locations for measurements are at the inlet end, at one-third, at two-

third and near the far end of laterals and manifold. Detailed form given by Merrian and Keller

(1978) may be helpful in data collection.

Example 8.2: Data was collected on a lateral of a trickle irrigation system at different

pressures as shown below.

Calculate and compare different factors of the system. Emitters were orifice type. Assume

discharge correction factor (DCF) is 1.0 for simplicity (see Merriam and Keller, 1978, P. 137-

139).

Average volume collected per minute at

Pressure

(m)

Inlet end 1/3 down 2/3 down Far end

5 (3.52) 48.0 2.88 51.5 3.09 53.0 3.18 57.5 3.45

15 (10.56) 121 5.26 131 7.86 119 7.14 116 6.96

25 (17.60) 146 8.76 145 8.70 147 8.82 150 9.0

Sample calculations for 5 psi low – one quarter = 2.88 lph

Average discharge (2.88 + 3.09 + 3.18 + 3.45) = 3.15 lph

Emission Uniformity = Minimum rate of discharge per plantAverage rate of discharge per plant

= 2.88 x 100 = 91.4%3.15

PELQ = 0.9 EU = 0.9 x 91.4 = 82.3%

Exponents, x1 = log (q1/q2)log (H1/H2)

= log (2.88/5.26)log (3.52/10.56)

= 0.55

129

By rearranging the above equation

Kd = q/H* or

Kd1 = 2.88 = 1.44

3.520.55

System PELQ

Efficiency Reduction Factor, ERF = 1/DCF = 1

System PELQ = ERF x Test PELQ

= 1 x 82.3

= 82.3%

Control of CloggingClogging of emitters is very difficult to control. It is difficult to detect in the field and

expensive to clean or replace the clogged emitters. Clogging may be caused by suspended

particles of sand, silt, clay and debris. Small particles deposit in low-velocity areas in the

different parts of the trickle system. With passage of time these particles gather mass due to

coagulation and occur may often clog the system. Clogging if irrigation water contains high

amount of soluble salts such as calcium, magnesium, carbonates, bicarbonates and sulphides.

Sometime growing of algae and bacteria may also clog the system.

Thus appropriate measures are essential to prevent clogging. Suspended particles can

be removed by using settling ponds and filters. Periodic flushing of pipes, emission devices

and filters is also helpful to check clogging. Chemical treatments by algaecides and bacteria-

cides are used to control biologically caused clogging.

FiltrationRemoval of suspended particle is essential for satisfactory performance of trickle

system. The suspended material that can plug the emitters may be inorganic or organic. The

organic material includes algae, bacteria, larvae, fish, snails, and different parts of plants. The

major inorganic solids are sand, silt and clay particles. Settling basins, sand and screen filters,

cartridge and centrifugal separators are commonly used to remove suspended material.

Settling Basins: Settling basins, ponds or reservoirs can remove large volume of suspended

particles. Longer detention time is needed to remove smaller particles and vice versa.

Removal of clay particles is accelerated by using flocculating agent e.g. alum or poly-

electrolytes. The settling basins may need to be cleaned several times in a year depending

upon sediments in irrigation water. In addition to this, algae growth and wind blown

130

contaminants can be severe problems in settling basins. Due to these setbacks, setting basins

should be used only in extreme conditions.

Sand Filters: Sand or sand media filters are commonly used to remove heavy load of organic

and inorganic materials. These filters consist of cylindrical tanks having layers of sand and

fine gravel. Performance of these filters depends on water quality, flow rate, allowable

pressure drop, and sizes of sand used. The maximum recommended pressure drop across a

sand filter is about 70 Kpa (10 psi). Back flushing should be frequent enough to avoid

excessive pressure drop. Cleaning of the filters may be either manually or automatically.

Automatic systems should have at least two tanks. Out of this one is operating while the other

is being back-flushed as shown in Fig. 8.7.

(a) (b)

Figure 8.7 A sand media filter: a) Filtering process, b) Back process

(Source: James, 1988, p.290)

Centrifugal Separators: Centrifugal filters are also called sand or cyclonic separators. They

use centrifugal force to remove and eject high density particles from water. However,

centrifugal separators are not effective to remove organic contaminants. These filters should

be placed upstream of sand, screen and cartridge filters that remove finer particles and

organic materials.

Screen Filters: Long cylindrical filters made of stainless steel or nylon are the most common

type of filters used with trickle systems. Like sand filters, the screen filters should be

frequently washed for proper functioning of the filters.

Cartridge Filters: These filters can remove organic materials and extremely fine particles

that cannot be removed by other filters. Cartridge may be disposable or washable that is

usually made of nylon, cotton and fibreglass.

131

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University, USA.

Callies, R.E. 1978. Corner pivot, an effective corner watering system. ASAE Paper No. 78-2006.

Christiansen, J.E. 1942. Irrigation by sprinkling. University of California, Berkely, Bull. 670.

Ghinassi G. 2008. Manual for performance evaluation of sprinkler and drip irrigationsystems. International Commission on Irrigation and Drainage (ICID Publication No. 94),New Delhi, India

Heermann, D.F. and P.R. Hein. 1968. Performance characteristics of self propelled centerpivot sprinkler irrigation system. Trans. ASAE 11: (1) 11-15.

James, Larry, G. 1988. Principles of farm irrigation system design. John Wiley & Sons, NewYork, U.S.A.

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Merkley, G. P. and Allen, R. G. 2007. Sprinkler and trickle irrigation, Lecture Notes.Biological and Engineering Department, Utah State University, USA.

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Phocaides, A. 2000. Technical handbook on pressurized irrigation techniques. Food andAgriculture Organization of the United Nations.

Ring, L., and D.F. Heermann. 1978. Determining center pivot sprinkler uniformities. ASAEPaper No. 78-2001.

Sne, Moshe. 2006. Guidelines for planning and design of micro irrigation in arid and semi-arid regions. International Commission on Irrigation and Drainage, India.

Splinter, W.E. 1976. Center pivot irrigation. Scientific American. Vol. 234, No. 6, pp.90-99.

Watters, G.Z., and Keller, J. 1978. Trickle irrigation tubing hydraulics. ASCE Tech. PaperNo. 78-2015.

United States Department of Agriculture. 1960. SCS National Engineering handbook, Section15 Irrigation, Chapter 11 Sprinkler Irrigation, USDA, SCS, Washington, D.C. 83 p.