Chapter 3 _ Francis and Kaplan Turbine _ Fluid Machinery

2/3/13 Chapter 3 : Francis and Kaplan Turbine | Fluid Machinery

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Chapter 1 : General Concepts

Chapter 2 : Pelton Turbine

Chapter 3 : Francis and Kaplan

Turbine

Chapter 4 : Centrifugal Pumps

Chapter 5 : Similarity Relations

and Performance

Characteristics

Chapter 6 : Reciprocating

Pumps

Chapter 7 : Hydraulic devices

and Systems

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Chapter 3 : Francis and Kaplan Turbine

Q. 1. Discuss briefly the guide mechanism in reaction turbines.

Ans. It consists of a stationary circular wheel all round the runner of

the turbine. The stationary guide vanes are fixed on guide mechanism

The guide vanes allow the water t” strike the vanes fixed on the runner

without shock at inlet. The width between two adjacent vanes of guide

mechanism can be altered so that the amount of water striking the

runner can be varied.

Q. 2. List the advantages of Kaplan Turbine over Francis

Turbine.

Ans. Advantages of Kaplan turbine over Francis turbine

(i) Runner vanes are adjustable in Kaplan turbine while in Francis

turbine run vanes are not adjustable.

(ii) There is less resistance offered as the number of vanes are fewer in

Kaplan turbine (in) Specific speed range 250-850 m Kaplan turbine In

Francis turbine specific speed range is 5o—250.

Q. 3. Draw velocity triangles at inlet and outlet of typical

Francis turbine vane.

Ans. There are three types of velocity triangles for. inlet and outlet in

Francis turbine. Triangles are made for slow runner, medium runner

and fast runner.

Fig. Slow runner

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Fig. Medium Runner

Fig. Fast Runner

Q. 4. Define degree of reaction and Euler’s Head.

Ans. The degree of reaction (R) is defined as a ratio of change of

pressure energy in the runner to the change of total energy in the

runner per kg of water.

Euler’s Head: It is defined as energy transfer per unit weight.

Q.5. Why is the efficiency of Kaplan turbine nearly constant

irrespective of speed variation under load?

Ans. Kaplan turbines has the concept of adjusting the runner vanes in

the face of changing load conditions on the turbine, with proper

adjustment of blades during its running the Kaplan turbine is capable of

giving a constant and high efficiency for a wide range of load

conditions. The pitch of the blades is also automatically adjusted by the

governor through the action of a servo meter.

Q. 6. Define specific speed of a turbine and write down its

expression.

Ans. The specific speed of a turbine may be defined as the speed of an

imaginary turbine, identical with the given turbine which will develop a

unit power under a unit head.

It is given by

N = Speed of the runner in r.p.m.

H =Head of water

P = Power produced.

Q. 7. Sketch different types of draft tubes.

Ans. Following are the important types of draft tubes which are

commonly used.

1. Conical draft tubes



2. Simple elbow tubes

3. Moody spreading tubes

4. Elbow with circular inlet and rectangular outlet.

Fig. Types of draft tubes

Q. 8. List the various functions of surge tanks.

Ans. Surge tanks have the following functions:

1. To control the pressure variations, due to rapid changes in the

pipeline flow, thus eliminating water hammer possibilities.

2. To regulate the flow of water to the turbines.

3. To reduce the distance between the free water surface and turbine,

thereby reducing the water hammer effect on penstock.

4. It protects up stream tuner from high pressure rises.

Q. 9. Explain (i) Hydraulic efficiency (ii) Mechanical efficiency

(iii) Overall efficiency of turbines.

Ans. (i) Hydraulic Efficiency-It is the ratio of work done on the wheel

to the head of rater (or energy) actually supplied to the turbine i.e.

(ii) Mechanical Efficiency—it is the ratio of actual work available at

the turbine to e energy imparted to the wheel.

(iii) Overall Efficiency—it is a measure f the performance of a

turbine and is the 120 of power produced by the turbine to the energy

actually supplied to the turbine.

Q. 10. Differentiate between Francis and Kaplan turbine.

Ans.

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Ans.

Q. 11. List the unit quantities as applied to turbo-machines.

Ans. (i) Unit power (ii) Unit speed (iii) Unit discharge.

Unit Power-The powered developed by a turbine working under a

head of 1 meter, is known as unit power:

P =Power developed,

H =Head of water

Unit Speed-The speed of turbine, working under a head of 1 meter, is

known as unit speed

N = speed of turbine,

H = Head of water

Unit Discharge-The discharge of a turbine, working under a head of 1

meter, is known as unit discharge.

Q = Discharge,

= Head of water

Q. 12. List the factors/criteria to choose a turbine.

Or

How to decide whether Kalpan, Francis or a pelton type tupe

turbine would be used in a hydro project?

Ans. The selection of turbines depend on the following considerations.

1. Operating Head— Pelton turbine - Greater than 400 m

Francis turbine - 50-400 m

Kaplan turbine - Less than 50 m

2. Specific speed-Turbine having high specific speed is selected. High

speed means a smaller size of the turbine. Francis turbines run at

higher speeds (50—250) than those of pelton wheels (8—50), Kaplan

turbine have the greatest specific speed (250—1000).

3. Cavitation- Cavitation occurs when the pressure at the runner

outlet equals vapour pressure. Francis turbines can not be used for

very high heads because of cavitation. Pelton turbines are free from

cavitation because the pressure at runner outlet is the atmospheric.

4. Performance characteristics—Turbines should be selected in such

a way that their efficiencies do not fall appreciably when operating

under part load. Francis turbines operate efficiently between half and

full load. Kaplan turbines are more efficient at low heads.

5. Overall cost—The plant should be designed for the minimum cost

as cost is the prime consideration in designing a plant

6. Number of units—It is better to go in for a larger unit as far as

possible, but there must be at least two units at any particular site so

that one unit is always available.

Q. 13. What is the importance of a draft tube in a Francis

turbine 7 Discuss different types of draft tubes.



Ans. It is a pipe, which connects the turbine and outlet or tail race,

through which the water exhausted from the runner, flows to the outlet

channel.

It also act as a water conduit.

Draft tube has the following important function:

1. It makes the installation possible above the tail race level without

the loss of head.

2. Water velocity at runner outlet is very, high. By using draft tube the

velocity can be lowered. Loss of kinetic energy is converted into

pressure energy.

3. Draft tube prevents the splashing of water coming out of the runner.

Different types of draft tubes used are:

(1) Conical draft tubes

(2) Simple elbow tubes

(3) Moody spreading tubes

(4) Elbow with circular inlet and rectangular outlet.

Fig. Types of draft tubes

(1) Conical Draft Tubes—This is known as tapered draft tube and

used in all reaction turbines where conditions permit. It is preferred for

low specific speed and Francis turbine. The maximum cone angle is 8°

(a = 40°). The hydraulic efficiency is 90%.

(2) Simple Elbow Tubes-The elbow type draft tube is often preferred

in most of the power plants. If the tube is large in diameter; ‘it may be

necessary to make the horizontal portion of some other section. A

common form of section used is over or rectangular. It has low

efficiency around 60%.

(3) Moody Spreading Tubes-This tube is used to reduce the whirling

action of discharge water when turbine runs at high speed under low

head conditions. The draft tube has efficiency around 85%.

(4) Elbow with circular inlet and rectangular outlet—This tube

has circular cross- section at inlet and rectangular section at outlet. The

change from circular section to rectangular section take place in the

bend from vertical leg to the horizontal leg. The efficiency is about

85%.

Q. 14. Derive the expression for specific speed of turbine. What

is the range of specific speed for reaction turbine?

Ans. Power available at turbine shaft



Since and w are constant: … (1)

The tangential velocity u, the flow velocity the absolute velocity v

and the head H on the turbine are related as

Now

Also

Substituting this value in expression (1)

…

(2)

Where k is constant of proportionality

Now taking H =1, P= 1, then (specific speed)

Expression (ii) may be written as

Specific speed,

Specific speed for Francis turbine = 50 — 250.

Specific speed for Kaplan turbine = 250 — 850.

Q. 15. Show that in a given turbine v

H = available head, u tangential velocity, Q = discharge, P

power developed.

Ans. (i) We know that

Absolute velocity v

…

(1)

Also tangential velocity, … (2)

So from (1) and (2)

(ii) Q = Area of flow x Velocity

So

(iii)



so (hence proved).

Q. 16. Define draft tube efficiency. Give mathematical

expression.

Ans. The efficiency of the draft tube is defined as the ratio of actual

conversion of kinetic head into pressure head in the draft tube to the

kinetic head at the inlet of the draft tube.

Mathematically, = =

Q .17. Why the draft tube is not used for Pelton turbine?

Ans. In case of pelton turbine all the K. E. is lost and draft tube is not

used because the pressure value is just the atmospheric so there is no

requirement of draft tube.

Q .18. What is the function of scross casing in reaction

turbines?

Ans. Scroll casing provides the limited area around the runner to

maintain the constant velocity of water flow around the runner The

material of scroll casing may be cost steel, cast iron, concrete or

concrete and steel.

Q.19. Explain with neat sketch the operation of Kaplan turbine,

governing of Kaplan turbines and their performance

characteristics.

Ans. Kaplan Turbine The figure shows a schematic diagram of Kaplan

turbine The function of the guide vane is same as in case of Francis

turbine Between the guide vanes and the runner, the fluid in a

propeller turbine turns through a right-angle into the axial direction and

then passes through the runner. The runner usually has four or six

blades and closely resembles a ship’s propeller Neglecting the frictional

effects, the flow approaching the runner blades can be considered to be

a free vortex with whirl velocity being inversely proportional to radius,

while on the other hand, the blade velocity is directly proportional to

the radius The take care of this different relationship of the fluid

velocity and the blade velocity with the changes in radius, the blades

are twisted. The angle with axis is greater at the tip that at the root.



Performance Characteristics of Reaction Turbine:

It is not always possible in practice, although desirable, to run a

machine at its maximum efficiency due to changes in operating

parameters. Therefore, it becomes important to know the performance

of the machine under conditions for which the efficiency is less than the

maximum It is more useful to plot the basic dimensionless

performance parameters (Fig 1) as derived earlier from the similarity

principles of fluid machines Thus one set of curves, as shown in Fig 1, is

applicable not just to the conditions of the test, but to any machine in

the same homologous series under any altered conditions.

Fig.I: Performance characteristics of a reaction turbine in

dimensionless parameters)

Figure 2 is one of the typical plots where variation in efficiency of

different reaction turbines with the rated power is shown.

Fig. 2 Variation of efficiency with load

Governing of Reaction Turbines- Governing of reaction turbines is

usually done by altering the position of the guide vanes and thus

controlling the flow rate by changing the gate openings to the runner.

The guide blades of a reaction turbine are pivoted and connected by

levers and links to the regulating ring. Two long regulating rods, being

attached to the regulating ring at their one ends, are connected to a

regulating lever at their other ends. The regulating lever is keyed to a

regulating shaft which is turned by a servomotor piston of the oil.



Q. 20. Write note on Surge tanks.

Ans. A surge tank is a storage reservoir fitted at some opening made

on a long penstock to receive the rejected flow when the penstock is

suddenly closed by a value fitted at its steed end. Surge tanks, relieves

the pipe line of excessive pressure produced due to closing of the

penstock, thus eliminating positive water hammer effect by admitting

in it a large mass of water which would have flown out of the pipe line.

It is also used in a large pumping plant to control variations

resulting from rapid changes in the flow.

Functions of surge tanks:

(1) To control the pressure variations by reliving the line of excessive

pressure.

(2) Regulation of flow in power plants and pumping plants.

(3) Regulation of turbine speed.

Location of surge tank: Theoretically it should be located close to a

power or pumping plant. It is generally located at the junction of

pressure tunnel and penstock or on the side of the mountain.

Types of surge tanks:

(1) Single surge tanks

(2) Restricted orifice type

(3) Differential type.

Q. 21. Write short note on design of runner for reaction

turbine.

Ans. Suppose, H = Head

N = Running Speed

P = Power Output

The design Procedure is given as follows.

1. Assume probable values of

Hydraulic efficiency.

Overall efficiency

n, Ratio of width to diameter

Flow ratio

2. Find Discharge by using

Shaft Power

3. Area through which water enters

Where and are entrance diameter and width.

is effect for the vanes.

4. Find tangential velocity



5. Find Flow Velocity,

6. Obtain and by using

Assume

Use continuity equation

(1) Net Head, H =

(2) Hydraulic efficiency,

(3) Discharge through Kaplan turbine:

Problem 1. A Francis turbine works under a head of 25 m

producing 3675 kW at 150 r.p.m. Determine the (a) Unit power

and unit speed of the turbine (b) Specific speed of the turbine

and (c) Power developed by this turbine if the speed is

reduced to 100 r.p.m.

Solution. P= 3675 kW

H=25m

N = 150 r.p.m.

Unit power and unit speed

Unit power:

Unit speed:

Specific speed of the turbine

= 162.66

=163 r.p.m.

Power developed if the speed reduced to 100 r.p.m.

We know that



Also

Problem. 2. A Kaplan turbine runner is to be designed to

develop 7357.5 kW shaft power. The net available head is 5.50

m. Assume that the speed ratio is 2.09 and flow ratio is 0.68

and the overall efficiency is 60%. The diameter of the boss is

rd of the diameter of the runner. Find the diameter of the

runner, its speed and its specific speed.

Solution: Given:

Shaft power P = 7357.5 kW

Head H = 5.50m

Speed ratio

Flow ratio

Overall efficiency, = 60% = 0.60

Diameter of boss,

Using relation

0.60 =

We have



6.788m

And 6.788 = 2.262 m

Using

= 61.08 r.p.m.

Specific speed is given by

= 622 r.p.m.

Problem. 3. The following data pertains to an inward flow

reaction turbine Net head = 60 m, speed = 650 r.p.m., Brake

power = 275 kW Ratio of wheel width to wheel diameter at

inlet = 0.10 Ratio of inner diameter to outer diameter =

0.5 Flow ratio = 0.17, = 0.95 and = 0.85. The flow

velocity remains constant and the discharge is radial.

Neglecting area blockage by blades, work out the main

dimensions and blade angles of the turbine.

Solution:

Flow velocity = =5.83m/s

=5.83m/s

Power available from the turbine shaft = w Q H x

275 x = (9810 x Q x 60) x 0.85

Discharge through the turbine,

= 0.55 /s

Also

0.55 = x 0.1 d x 5.83

Diameter of wheel at inlet, = 0.5486m = 54.86cm

Width of wheel at inlet, = 0.1 x 54.86 = 5.486 cm.

Diameter of wheel at outlet, = 0.5 d = 0.5 x 54.86 = 27.43 cm

Since the discharge of water at inlet and outlet tips is same,

Width of wheel at outlet, = 0.1097 m = 10.97 cm

Angles at inlet:

Peripheral velocity at inlet, = 18.66 m/s

Hydraulic efficiency,




0.9 5

Angles at outlet:

0.6248,

Problem 4. A Francis turbine with an overall efficiency of 75%

is required to produce 14825 kW power. It is working under a

head of 7.62 m. The peripheral velocity = 0.26 and the

radial velocity of flow at inlet are 0.96 . The wheel runs at

150 r.p.m. and the hydraulic losses in the turbine are 22% of

the available energy. Assume Radial discharge, determine

(i) The guide blade angle

(ii) The wheel vane angle at inlet

(iii) Diameter of the wheel at inlet, and

(iv) Width of the wheel at inlet.

Solution: Overall efficiency, =

Power produced = 148.25 kW

Head = 7.62 m

Peripheral velocity,

= 3.179 m/s

Velocity of flow at inlet,

= 11.738 m/s



Speed, N = 150 r.p.m.

Hydrauls losses = 22% of available energy

Discharge at outlet = Radial

Hydraulic efficiency is given as

=0.78

=0.78

= 18.34 m/s

1. The guide blade angle, a

=0.64

0.64 = 32.619°

2. The wheel vane angle at inlet,

=0.774

0.774 = 37.74

3. Diameter of wheel at inlet

=0.4047m

4. Width of the wheel at inlet

w.P.

= 2.644

Using

2.644 = x 0.4047 x x 11.738



2.644 = x 0.4047 x x 11.738

= 0.177m

Problem 5. A hydro-turbine is required to give 25 mW at 50 m

heat and 90 r.p.m. runner speed. The laboratory facilities

available permit testing of 20 kW model at 5m head. What

should be the model runner speed and model prototype scale

ratio?

Solution: = 25 mW =20 kW

= 90 r.p.m. =5 m

=50m

Scale ratio = =6.29

=90x6.29x =179r.p.m.

Problem 6. In an inward flow reaction turbine having vertical

shaft, water enters the runner from the guide blades at an

angle of 155° with the runner blade angle at entry being 100°.

Both these angles are measure from the tangent at runner

periphery drawn in the direction of runner rotation. The flow

velocity through the runner is constant, water enters the draft

tube from tile runner without whirl and the discharge from the

draft tube into the tail race takes place with a velocity of 2.5

m/s. The runner has the dimensions of 40 cm external

diameter and 3.8 cm inlet width. The turbine works with a net

head of 35m and the loss of head in the turbine due to fluid n is

4m of water. Draw vector diagrams and calculate:

1. Speed of the runner

2. Runner blade angle at a point on the outlet edge where the

radius of rotation is 9 cm.

3. Power generated by the turbine and its specific speed.

4. Inlet diameter of the draft tube.

Solution. Velocities at inlet and exit are related by the expression:

From the inlet velocity triangle



= (180—155) =25°

= (180 — 100) = 800

Since the discharge is in radial direction,

Work done = = 0.43

From the energy balance,

Head supplied

= (work done) + (kinetic heat at exit) + (losses in the

runner)

3.5 + +4

= 8.45m/s

= 1.968 = 1.968 x 8.45 = l6.63m/s

1. ;1663=

N = = 794 r.p.m.

2. From outlet velocity triangle:

=8.45m/s

Peripheral velocity of the outer edge at 9 cm radius

= 16.63 x = 7.48 m/s

= 1.13 ; vane angle at outlet, =

Discharge through the turbine, Q x 0.4 x 0.038 x 8.45

= 0.4035

3. Power developed by the turbine,

= 9810 x 0.4035 x 0.43 121.5 x W = 121.5 kW

Assume a mechanical efficiency of 98%

4. Power available at turbine shaft = 121. 5 x 0.98 = 119.07

Specific speed of the turbine, Ns = 101.77



Specific speed of the turbine, Ns = 101.77

5. Inlet area of draft tube = = = 0.04775

If d is the inlet diameter of the tube,

=0.04775

d= =0.246m

Problem.7. Francis turbine develops 365 kW at an overall

efficiency of 80%. When working under a static head of 5 m,

the draft tube being cylindrical and of diameter 2.5 m. What

increase in power and efficiency of the turbine would you

expect if a tapered draft tube having an inlet diameter of 4m

and efficiency of conversion of 90% is substituted for the

cylindrical one? It maybe presumed that head, speed and

discharge remain constant.

Solution Power available = wQH×

365 x = (9810 x Q x 5) x 0.8

Q=

When the draft tube is tapered one velocity of water at inlet to draft

tube

=1.89m/s

velocity of water at outlet of draft tube

=0.74m/s

Heat gained = xO.9 = 0.14 m

Increase in efficiency = = 0.028 = 2.8%

Increase in power = increase in efficiency x original power

= 0.028 x (9810 x 9.30 x 5)

=12773W=12.77kW

Problem.8. An inward flow reaction turbine discharges radially

and the velocity of flow is constant and equal to the velocity of

discharge from the turbine. Show that the hydraulic efficiency

can be expressed by

Where a and are respectively the guide vane angle and wheel

vane angle at Intel.

Solution. From the inlet velocity triangle



For radical discharge at outlet

Thus

Or

Substituting the value of , we get

Also substituting the value of u from above, we get

Now =

Or =

Or

Problem.9. The velocity of whirl at inlet to the runner of an

inward flow reaction turbine is (3.15 ) m/s and the velocity

of flow at inlet is (1.05 ) m/s. The velocity of whirl at exit is

(0.22 ) m/s in the same direction as at inlet and the velocity

of flow at exit is (0.83 ) where H is the head in meters. The

inner diameter of the runner is 0.6 times the outer diameter.

Assuming hydraulic efficiency of 80%, compute the angles of

the runner vanes at inlet and exit.

Solution.

From inlet velocity triangle, we have



1.9091

= 62°21’

From outlet velocity triangle, we have

=0.6194

=31°46’

Problem.10. The inlet and the outlet runner blade angles of a

propeller turbine are and 25° respectively to the tangential

direction of the runner. The inlet guide vane angle is 30°. The

speed of the turbine 30 rpm. The mean diameter of the runner

blades is 3.6 m and the area of flow is 30 . Assuming that the

velocity of flow is constant throughout, determine (1)

Discharge (ii) Power developed (iii) Hydraulic efficiency (iv)

Specific speed.

Solution.

=3.6m

N =30 r.p.m.

= 90°

= 25°

a = 30°

Flow area, a =

Runner blade angle at inlet is radial

As velocity of flow is constant so



= 5.65 m/s

Also

= 5.65 m/s

From inlet velocity triangle

=5.65xtan30°

=3.262m /s

=5.65m/s

From outlet velocity triangle,

tan 25°

+ 5.65 = =7 m/s

= 7 - 5.65 = 1.35 m/s

=3.529 m/s

We have,

[5.65 x 5.65 — 1.35 x 5.65]

H = 2.47 + 0.634 3.104 m

(1)Hydraulic efficiency is given by

=0.798 = 79.8%.

(2)Discharge through turbine, Q = Area of flow x Velocity of flow

=30x3262=97.86

(3)Power developed by turbine

× Weight of

water

x 1000 x 9.81 x 97.86

= 2378 kW

(4)Specific speed is given by 355.08 rpm

Problem.11. In a Francis turbine of very low specific speed, the

velocity of flow from inlet to exit of the runner remains

constant. If the turbine discharges radially, show that the



constant. If the turbine discharges radially, show that the

degree of reaction p can be expressed as

where a and are the guide and runner vane angles

respectively and the degree of reaction p is equal to the ratio of

pressure drop to the hydraulic work done in the runner,

assuming that the losses in the runner are negligible.

Solution. Applying Bernoulli’s equation between the inlet and exit of

the runner and neglecting the potential difference, we get

(for radial discharge)

Where and are the pressure heads at the inlet aid the exit of the

runner respectively.

Thus pressure head drop due to hydraulic work done in the runner is

given by

Now

Or

Or … (1)

For radical discharge

Also

Or u =V [cos a-sin a cot ]

And

Thus, introducing these values in equation (i) above and simplifying it,

we get.

Problem.12. A Francis turbine supplied through a 6 m diameter

penstock has the following particulars.

Output of installation 63500 kW

Flow 117

Speed 150 r.p.m.

Hydraulic efficiency 92%

Mean diameter of turbine at entry 4 m

Mean blade height at entry 1 m



Mean blade height at entry 1 m

Entry diameter of draft tube 4.2 m

Velocity in tail race 2.4 m/s

The static pressure head in the penstock measured before

entry to the runner is 57.4 m. The point of measurement is 3 m

above the level of the tail race. The loss in the draft tube is

equivalent to 30% of the velocity head at entry to it. The exit

plane of the runner is 2 m above the tail race an the flow leaves

the runner without swirl. Determine:

1. The overall efficiency,

2. The direction of flow relative to the runner at inlet,

3. The pressure head at entry to the draft tube.

Solution.

(a)The net head H for the turbine is given by equation

And 2.4 m/s.

Thus by substitution, we get

= 60.98 m

The overall efficiency is given by

= 0.907 or 90.7%

(b) Neglecting the vane thickness, the velocity of flow at inlet i given by

equation

B=1m; and D=4m


= 9.31 m/s

31.42 m/s

Or 0.92

17.52 m/s

The direction of flow relative to the runner at inlet is given by

=0.6698

(c) The pressure head at entry to the draft tube is given by equation

2m =8.44m/s; =2.4m/s



2m =8.44m/s; =2.4m/s

And =1.09 m


+1.090—4.25m

Problem.13. A model of Francis turbine one-fifth of full size,

develops 3 kW at 306 r.p.m. under a head of 1.77 m. Find the

speed and power of full size turbine operating under a head of

5.7 m, if (a) the efficiency of the model and the full size turbine

are same, (b) the efficiency of the model turbine is 76% and

the scale effect is considered.

Solution: (a) For the same efficiency of the model and the prototype

Or

=109.8 r.p.m.

Further

Or

=433.43kW

(b) According to Moody’s equation,

Or

Or

=114.5 r.p.m.

We know that

Or

=491.09 kw



Problem.14. Show that in a turbine, with radial vanes at inlet

and outlet, the hydraulic efficiency is given by:

Where is the guide blade angle. Assume the flow velocity to

remain constant.

Solution. Neglecting losses with in the runner, the energy balance

gives:

Head supplied = (work done or head utilized) + (kinetic head at exit)

For radial vanes at inlet and outlet


Problem.15. A Kaplan turbine develops 2250 kW under a net

head of 5.5 m and with overall efficiency 87 percent. The draft

tube has a diameter of 2.8 m at its inlet and has an efficiency

of 78 percent. In order to avoid cavitation, the pressure head



of 78 percent. In order to avoid cavitation, the pressure head

at entry to the draft tube must not drop more than 4.5 m below

atmosphere. Calculate the maximum height at which the

runner may be set above the tail race level.

Solution. Power available from the turbine shaft,

P = wQH x

2250 × = (9810 x Q x 55) x 0.87;

Q = 47.93

Now =7.79 m/s

Given: = 4.5m

=4.5-

Draft tube efficiency,

0.78 =

= 4.5 - x 0.78 = 2.087

Problem.16. An inward flow pressure turbine has runner vanes

which are radial-at the inlet and inclined backward at 45° to

the tangent at discharge. The guide vanes are inclined at 15°

to tangent at inlet and velocity of water leaving the guides in

24 m/sec. Determine correct speed for runner and absolute

velocity of water at point of discharge if diameter at entry is

twice that at discharge and width at entry is 0.6 times that at

discharge.

Solution.

Fig. Input and outlet velocity triangle

Given =15°

= 24 m/s

In outlet velocity triangle



In outlet velocity triangle

= m/s Ans.

We know

x33.94

x 33.94 = 28.28 m/s

(For radial discharge)

= 105.94 m/s Ans.

Chapter 3 _ Francis and Kaplan Turbine _ Fluid Machinery

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