H16 Losses in Piping Systems -...

H16 Losses in Piping Systems

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may occur from time to time. If any errors are discovered in

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SECTION 1.0

TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS

INTRODUCTION

One of the most common problems in fluid mechanics is the estimation of

pressure loss. This apparatus enables pressure loss measurements to be made on

several small bore pipe circuit components, typical of those found in central

heating installations. This apparatus is designed for use with the TecQuipment

Hydraulic Bench H1, although the equipment can equally well be supplied from

some other source if required. However, al1 future reference to the bench in this

manual refers directly to the TecQuipment bench.

1.1 Description of Apparatus

The apparatus, shown diagrammatically in Figure 1.1, consists of two separate

hydraulic circuits, one painted dark blue, one painted light blue, each one

containing a number of pipe system components. Both circuits are supplied with

water from the same hydraulic bench. The components in each of the circuits are

as follows:

Dark Blue Circuit

Light Blue Circuit

1. Gate Valve

2. Standard Elbow

3. 90° Mitre Bend

4. Straight Pipe

5. Globe Valve

6. Sudden Expansion

7. Sudden Contraction

8. lS0mm 90° Radius Bend

9. 100mm 90° Radius Bend

10. 50mm 90° Radius Bend

3. 4.


Key to Apparatus Arrangement

A Straight Pipe 13.7mm Bore

B 90° Sharp Bend (Mitre)

C Proprietary 90° Elbow

D Gate Valve

E Sudden Enlargement - 13.7mrn/26.4mm

F Sudden Contraction - 26.4mrn/13.7rnrn

G Smooth 90° Bend 50mm Radius

H Smooth 90° Bend 100mrn Radius

J Smooth 90° Bend lS0mm Radius

K Globe Valve

L Straight Pipe 26.4mm Bore

In all cases (except the gate and globe valves) the pressure change across each of

the components is measured by a pair of pressurized Piezometer tubes. In the case

of the valves pressure measurement is made by U-tubes containing mercury.

SECTION 2.0 THEORY

Figure 2.1

Figure 2.2

Figure 2.3

For an incompressible fluid flowing through a pipe the following equations apply:

(Continuity)

(Bernoulli)

Notation:

Q Volumetric flow rate (m3/s)

V Mean Velocity (m/s)

A Cross sectional area (m3)

Z Height above datum (m)

P Static pressure (N/m2)

hL Head Loss (m)

ρ Density (kg/m3)

g Acceleration due to gravity (9.81m/s2)

2.1 Head Loss

The head loss in a pipe circuit falls into two categories:

(a) That due to viscous resistance extending throughout the total

length of the circuit, and;

(b) That due to localized effects such as valves, sudden changes in

area of flow, and bends.

The overall head loss is a combination of both these categories. Because of

mutual interference between neighboring components in a complex circuit the

total head loss may differ from that estimated from the losses due to the

individual components considered in isolation.

Head Loss in Straight Pipes

The head loss along a length, L, of straight pipe of constant diameter, d, is

given by the expression:

where f is a dimensionless constant which is a function of the Reynolds

number of the flow and the roughness of the internal surface of the pipe.

Head Loss due to Sudden Changes in Area of Flow

Sudden Expansion: The head loss at a sudden expansion is given by the

expression:

( )


Sudden Contraction: The head loss at a sudden contraction is given by the

expression:

where K is a dimensionless coefficient which depends upon the area ratio

as shown in Table 2.1. This table can be found in most good textbooks on

fluid mechanics.

A2/A1 0 0.1 0.2 0.3 0.4 0.6 0.8 1.0

K 0.50 0.46 0.41 0.36 0.30 0.18 0.06 0

Table 2.1 Loss Coefficient For Sudden Contractions

Head Loss Due To Bends

The head loss due to a bend is given by the expression:

where K is a dimensionless coefficient which depends upon the bend

radius/pipe radius ratio and the angle of the bend.

Note:

The loss given by this expression is not the total loss caused by the bend

but the excess loss above that which would be caused by a straight pipe

equal in length to the length of the pipe axis.

See Figure 4.5, which shows a graph of typical loss coefficients.

Head Loss due to Valves

The head loss due to a valve is given by the expression:

where the value of K depends upon the type of valve and the degrees of

opening.

Table 2.2 gives typical values of loss coefficients for gate and globe valves.

Globe Valve, Fully Open 10.0

Gate Valve, Fully Open 0.2

Gate Valve, Half Open 5.6

Table 2.2

2.2. Principles of Pressure Loss Measurements

Figure 2.4 Pressurised Piezometer Tubes to Measure Pressure Loss

between Two Points at Different Elevations

Considering Figure 2.4, apply Bernoulli's equation between points 1 and 2:

but:

(2-1)

therefore

( )

(2-2)

Consider Piezometer tubes:

ρ [ ( )] (2-3)

also

(2-4)

giving

( )

(2-5)

Comparing Equations (2-2) and (2-5) gives

(2-6)

2.2.1 Principle of Pressure Loss Measurement

Considering Figure 2.5, since points 1 and 2 have the same elevation and pipe

diameter:

( ) = hL (2-7)

Consider the U-tube. Pressure in both limbs of the U-tube is equal at level 00.

Therefore equating pressure at 00:

( ) (2-8)


Figure 2.5 U- Tube Containing Mercury used to measure Pressure Loss

across Valves

giving ( )

(2-9)

hence:

( )

(2-10)

Considering Equations (2-7) and (2-10) and taking the specific gravity of

mercury as 13.6:

hL = 12.6x (2-11)

SECTION 3.0


INSTRUCTIONS FOR USE

(1) Connect the hydraulic bench supply to the inlet of the apparatus and

direct the outlet hose into the hydraulic bench weighing tank.

(2) Close the globe valve, open the gate valve and admit water to the Dark

Blue circuit by starting the pump and opening the outlet valve on

hydraulic bench.

(3) Allow water to flow for two or three minutes.

(4) Close the gate valve and manipulate all of the trapped air into the air

space in piezometer tubes. Check that the piezometer tubes all indicate

zero pressure difference.

(5) Open the gate valve and by manipulating the bleed screws on the U-

tube fill both-limbs with water ensuring no air remains.

(6) Close the gate valve, open the globe valve and repeat the above

procedure for the Light Blue circuit.

The apparatus is now set up for measurement to be made on the components

in either circuit.

The-datum position of the piezometer can be adjusted to any desired position either by pumping air into the manifold with the bicycle pump supplied, or by gently allowing air to escape through the manifold valve. Ensure that there are no water locks in these manifolds as these will tend to suppress the head of water recorded and so provide incorrect readings.

3.1 Filling the Mercury Manometer

Important:

Mercury and its vapors are poisonous and should be treated with great

care. Any local regulations regarding the handling and use of mercury

should be strictly adhered to.


Due to regulations concerning the transport of mercury, TecQuipment Ltd. are

unable to supply this item. To fill the mercury manometer, it is recommended

that a suitable syringe and catheter tube are used (not supplied) and the

mercury acquired locally.

If you are wearing any items of gold or silver, remove them.

Remove the manometer from the H16 before filling with mercury. The object

is to fill the dead-ended limb with a continuous column of mercury and then

invert the column so that a vacuum is formed in the closed end of the tube.

Hold the manometer upside down and support it firmly. Thread a suitable

catheter tube into the manometer tube, ensuring the catheter tube end touches

the sealed end of the glass column. Fill a syringe with 10ml of mercury and

connect to the catheter tube. Slowly fill the glass column using the syringe,

and as the mercury fills the column, withdraw the tube ensuring there are no

air bubbles left. Fill up to the bend and return the manometer to its normal

position. The optimum level for the mercury is 400mm from the bottom of the

U-Tube.

When the manometer has the correct amount of mercury in it, a small quantity

of water should be poured into the reservoir to cover the mercury and so

prevent vapors from escaping into the air.

3.2 Experimental Procedure

The following procedure- assumes that pressure loss measurements are to be

made on all the circuit components.

Fully open the water control valve on the hydraulic bench. With the globe valve

closed, fully open the gate valve to obtain maximum flow through the Dark Blue

circuit. Record the readings on the piezometer tubes and the U- tube. Collect a

sufficient quantity of water in the weighting tank to ensure that the weighing takes

place over a minimum period of 60 seconds.

Repeat the above procedure for a total of ten different flow rates, obtained by

closing the gate valve, equally spaced over the full flow range.


With simple mercury in glass thermometer record the water temperature in the

sump tank of the bench each time a reading is taken.

Close the gate valve, open the globe and repeat the experimental procedure for the

Light Blue circuit.

Before switching off the pump, close both the globe valve and the gate valve. This

procedure prevents air gaining access to the system and so saves time in

subsequent setting up.

.-

SECTION 4.0

4.1 Results


TYPICAL SET OF RESULTS AND CALCULATIONS

Basic Data

Bend Radii

Pipe Diameter (internal)

Pipe Diameter [between sudden expansion

(internal) and contraction]

Pipe Material

Distance between pressure tappings for straight

pipe and bend experiments

90° Elbow (mitre)

90° Proprietary elbow

90° Smooth bend

90° Smooth bend

90° smooth bend

= 13.7mrn

= 26.4mrn

Copper Tube

= 0.914m

=0

= 12.7mm

= 50mm

= 100mm

= 150mm

4.1.1 Identification of Manometer Tubes and Components

Manometer Tube

Number

Unit

1 Proprietary Elbow Bend

2

3 Straight Pipe

4

5 Mitre bend

6

7 Expansion

8

9 Contraction

10

11 150mm bend

12

13 100mm bend

14

15 50mm bend

16


4.2 Straight Pipe Loss

The object of this experiment is to obtain the following relationships:

(a) Head loss as a function of volume flow rate;

(b) Friction Factor as a function of Reynolds Number.

Test Time To Piezometer Tube Readings (cm) U-Tube

Number Collect 18 kg Water (cm) Hg

Water

(s) 1 2 3 4 5 6 Gate-Valve

1 63.0 51.0 14.0 49.5 16.3 86.9 29.2 29.4 28.6*

2 65.4 52.5 18.2 50.3 19.5 87.5 33.2 31.9 25.9

3 69.4 51.9 21.6 49.7 21.6 86.5 37.3 33.8 24.0

4 73.9 52.2 25.1 49.2 24.0 85.5 41.7 35.8 22.0

5 79.9 53.1 29.4 48.6 27.0 84.2 47.1 38.1 19.5

6 88.8 53.4 33.4 48.0 29.7 83.0 52.1 40.5 17.0

7 99.8 53.2 36.5 46.6 31.7 81.6 56.8 42.7 14.8

8 111.0 52.6 39.2 46.1 33.7 80.0 59.8 44.0 13.5

9 146.2 52.6 44.4 54.4 37.7 78.4 66.1 47.3 10.3

10 229.8 52.9 49.1 45.0 41.5 77.4 72.0 50.3 7.3

* Fully Open

Water Temperature 23°C

Table 4.1 Experimental Results for Dark Blue Circuit

Specimen Calculation

From Table 4.1, test number 1

Mass flow rate

Head loss


Volume flow rate (Q)

⁄

Area of flow (A)

Mean Velocity (V)

Reynolds Number (Re)

For water at 23°C ⁄

Therefore Re

Friction Factor (f)

Figure 4.1 shows the head loss - volume flow rate relationship plotted as a

graph of log hL against log Q.

The graph shows that the relationship is of the form hL α Qn with n = 1.73


This value is close to the normally accepted range of 1.75 to 2.00 for turbulent

flow. The lower value n is found as in this apparatus, in comparatively

smooth pipes at comparatively low Reynolds Number.

Figure 4.2 shows the Friction Factor - Reynolds Number relationship plotted

as a graph of friction factor against Reynolds Number.

The graph also shows for comparison the relationship circulated from

Blasius's equation for hydraulically smooth pipes.

Blasius's equation:

f

⁄ In the range 104 < Re < 105

As would be expected the graph shows that the friction factor for the copper

pipe in the apparatus is greater than that predicted for a smooth pipe at the

same Reynolds Number.

Figure 4.1 Head Loss - Volume Flow Rate

5. TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS

Figure 4:2 Friction Factor - Reynolds Number

4.3 Sudden Expansion

The object of this experiment is to compare the measured head rise across a

sudden expansion with the rise calculated on the assumption of:

(a) No head loss;

(b) Head loss given by the expression:

( )


Test Time To Piezometer Tube Readings (cm) V-Tube


Water

(s) 7 8 9 10 11 Globe Valve

11 73.2 38.7 43.5 42.5 12.1 38.3 37.4 20.2

12 76.8 39.2 43.5 42.5 22.1 38.5 38.5 19.0

13 82.6 39.1 43.0 42.2 24.5 38.3 40.2 17.4

14 95.4 39.4 42.0 41.5 28.5 38.3 43.0 14.7

15 102.6 39.7 42.2 41.7 30.2 38.0 44.0 13.6

16 130.8 40.0 41.5 41.1 33.8 37.3 46.5 11.7

17 144.6 40.4 41.5 41.2 35.2 37.5 47.5 10.1

18 176.9 40.7 41.4 41.2 37.0 37.3 49.1 8.6

19 220.8 41.0 41.5 41.4 38.6 37.4 50.2 7.5

20 277.8 41.2 41.6 41.6 39.6 37.5 51.4 6.5

Table 4.2(a) Experimental Results For Light Blue Circuit

Table 4.2(b) Experimental Results For Light Blue Circuit (continued)

Test Time To Piezometer Tube Readings (cm) V-Tube


Water

(s) 12 13 14 15 16 Globe Valve

11 73.2 12.1 35.0 7.2 32.1 3.8 37.4 20.2

12 76.8 14.1 34.9 9.7 32.5 6.0 38.5 19.0

13 82.6 17.0 34.9 12.6 31.6 8.6 40.2 17.4

14 95.4 22.0 34.5 17.6 31.5 13.7 43.0 14.7

15 102.6 23.6 34.2 19.4 30.7 15.2 44.0 13.6

16 130.8 28.0 33.4 23.7 29.6 19.5 46.5 11.7

17 144.6 29.7 33.4 25.5 29.8 21.4 47.5 10.1

18 176.9 31.9 33.2 27.7 29.4 23.5 49.1 8.6

19 220.8 33.6 33.3 39.4 29.5 25.4 50.2 7.5

20 227.8 35.0 33.4 30.9 29.5 26.8 51.4 6.5



From Table 4.2 test number 11.

Measured head rise = 48mm

(a) Assuming no head loss

(

)

(Bernoulli) Since

[ ( ⁄ )

]

[ ( )

]

From the table,

(Continuity)

= 1.67m/s

therefore h2 - h1

= [ ( )

]

= 0.132m


Therefore head rise across the sudden expansion assuming no head

loss is 132mm water.

(b) Assuming

( )

(

)

(Bernoulli)

(

)

( )

On rearranging and inserting values of d. = 13.7mm and d2 = 26.4mm,

this reduces to

which when

V1 = 1.67m/ s

gives

Therefore head rise across the sudden expansion assuming the simple

expression for head loss is 56mm water.

Figure 4.3 shows the full set of results for this experiment plotted as a graph

of measured head rise against calculated head rise.

Comparison with the dashed line on the graph shows clearly that the head

rise across the sudden expansion is given more accurately by the assumption of a

simple head loss expansion than by the assumption of no head loss.


Figure 4.3 Head Rise Across a Sudden Enlargement

4.4 Sudden Contraction

The object of this experiment is to compare the measured fall in head across a

sudden contraction, with the fall calculated in the assumption of:

(a) No head loss;

(b) Head loss given by the expression



From Table 4.2, test number 11.

Measured head fall = 221mm water

(a) Assuming no head loss

Combining Bernoulli's equation and the continuity equation gives:

[ ( )

]

Which when V2 = 1.67m/s gives

Therefore head fall across the sudden contraction assuming no head

loss is 132mm water.

(b)

Assuming

[ ( )

]

[ ( )

]


From Table 1, when

K = 0.376

giving

Which when V2 = 1.67m/s gives

h1 – h2 = 0.185m _

Therefore head fall across the sudden contraction assuming loss

coefficient of 0.376 is 18.5cm water.

Figure 4.4 shows the full set of results for this experiment plotted as a graph

of measured head fall against calculated head fall.


Figure 4.4 Head Decrease across a Sudden Contraction

The graph shows that the actual fall in head is greater than predicted by the

accepted value of loss coefficient for this particular area ratio. The actual

value of loss coefficient can be obtained as follows:

Let hm = measured fall in head and K' = actual loss coefficient

then

Calculated decrease in head (cm of water)


hence

which when

4.5 Bends

v2 = 1.67 m/s gives K' = 0.63

The aim here is to measure the loss coefficient for five bends. There is some

confusion over terminology, which should be noted; there are the total bend

losses (KL hL) and those due solely to bend geometry, ignoring frictional

losses (KB, hB).

i.e.

(Total measured head loss - straight line loss)

i.e.

(Head gradient for bend - k x head gradient for straight pipe)

Where k = 1 for KB

For either,

Plotted on Figure 4.5 are experimental results for KB and KL for the 5 types of

bends and also some tabulated data for KL. The last was obtained from

'Handbook of Fluid Mechanics' by VL Streeter. It should be noted though,

that these results are by no means universally accepted and other sources

give different values. Further, the experiment assumes that the head loss is

independent of Reynolds Number and this is not exactly correct. 6.

Figure 4.5 Graph of Loss Coefficient

Is the form of Kg what you would expect? Does putting vanes in an elbow

have any effect? Which do you consider more useful to measure, KL or KB?

4.6 Valves

The object of this experiment is to determine the relationship between loss

coefficient and volume flow rate for a globe type valve and a gate type valve.


Globe Valve

From Table 4.2, test number 11.

Volume flow rate = (valve fully open)

U-tube reading = mercury

Therefore hL =

= water

Velocity (V) =

Giving K =

= 15.3

Figure 4.6 shows the full set of results for both valves in the form of a graph of loss

coefficient against percentage volume flow.

TECQUIPMENT H16 LOSSES IN PIPING SYSTEMS Percentage Flow Rate

Figure 4.6 Loss Coefficients for Globe and Gate Valves

7.

8.


Normal manufacturing tolerances assume greater importance when the

physical scale is small. This effect may be particularly noticeable in relation

to the internal finish of the tube near the pressure tappings. The utmost care

is taken during manufacturing to ensure a smooth uninterrupted. Bore of the

tube in the region of each pressure tapping, to obtain maximum accuracy of

pressure reading.

Concerning again all published information relating to pipe systems, the

Reynolds Numbers are large, in the region of 1 x 105 and above. The

maximum Reynolds Number obtained in these experiments, using the

hydraulic bench, HI, is 3 x 104 although this has not adversely affected the

results. However, as previously stated in the introduction to this manual, an

alternative source of supply (provided by the customer) could be used if

desired, to increase the flow rate. In this case an alternative flow meter would

also be necessary.

The three factors discussed very briefly above are offered as a guide to

explain discrepancies between experimental and published results, since in

most cases all three are involved, although much more personal investigation

is required by the student to obtain maximum value from using this

equipment.

In conclusion the general trends and magnitudes obtained give a valuable

indication of pressure loss from the various components in the pipe system.

The student is therefore given a realistic appreciation of relating experimental

to theoretical or published information.

SECTION 5.0 GENERAL REVIEWS OF THE EQUIPMENT AND

RESULTS

An attempt has been made in this apparatus to combine a large number of pipe components

into a manageable and compact pipe system and so provide the student user with the

maximum scope for investigation. This is made possible by using small bore pipe tubing.

However, in practice, so many restrictions, bends and the like may never be encountered in

such short pipe lengths. The normally accepted design criteria of placing the downstream

pressure tapping 30-50 pipe diameters away from the obstruction i.e. the 90° bends, has been

adhered to. This ensures that this tapping is well away from any disturbances due to the

obstruction and in a region where there is normal steady flow conditions. Also sufficient pipe

length has been left between each component in the circuit; to obviate any adverse influence

neighboring components may tend to have on each other.

Any discrepancies between actual experimental and theoretical or published

results may be attributed to three main factors:

(a) Relatively small physical scale of the pipe work;

(b) Relatively small pressure differences in some cases;

(c) Low Reynolds Numbers.

The relatively small pressure differences, although easily readable, are encountered on the

smooth 90° bends and sudden expansion. The results on these components should therefore be

taken with most care to obtain maximum accuracy from the equipment. The results obtained

however, are quite realistic as can be seen from their comparison with published data, as

shown in Figure 4.5. Although there is wide divergence even amongst published data, refer to

page 472 of “Engineering Fluid Mechanics”, it is interesting to note that all curves seem to

show a minimum value of the loss coefficient 'K' where the ratio"

" is between 2 and 4. It is

important to realize and remember throughout the review of the results that all published data

have been obtained using much larger bore tubing (76mm and above) and considering each

component in isolation and not in a compound circuit.

. by Charles Jaeger and published by Blackie and Son L

H16 Losses in Piping Systems -...

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