1.

The pressure head from the reservoir level up to the centre line of a pelton wheel installation is
220m. The efficiency of the power transfer of the pipe plus the nozzles is 90%. There are two
nozzles and the wheel diameter is 1,5m. The relative exit velocity is 90%of the relative inlet
velocity and the deflection angle is is 165 degrees. The wheel develops 3 950 KW(hydraulic
power) at 375r/min. Determine

(a) The efficiency of the wheel

(b) The diameter of each jet

Answers (93%, 149 mm)

2. The supply pipe to a pelton wheel is 10km long and 1 min diameter. If the turbine wheel has an
efficiency of 83%, calculate the power delivered by the turbine if the reservoir is 650 m above the
jet and the jet has a diameter of 160mm. Take f as 0,004 and ignore losses in the nozzle. Determine
also the diameterof the turbine wheel if it has a rotational speed of 360r/min. Assume that
maximum power is developed by the wheel and the bucket exit angle is 15 degrees.

Answers (10,35MW, 2.84 m)

3, A pelton wheel installation uses a water jet of 75mm diameter to drive a wheel with the buckets
on a diameter of 0,9m. the deflection angle of the buckets is 160 degrees. the relative velocity of
the water is reduced by 12% while moving across the buckets, the rotational speed is 320r/min,
the total pressure behind the nozzle is 0,7 mpa and the velocity coefficient of the nozzle is 0,98.
Determine the hydraulic power developed by the wheel , the hydraulic efficiency of the wheel and
the overall efficiency of the turbine if the mechanical efficiency of the wheel is 96%.

answers(96,36kw, 88,4%, 81,57%)

4. The available pressure head foa francis turbine is 22m. the rotor blades are radial at the inlet and
curved backward at the exit. the outside diameter is 1,5 times the inside diameter and the velocity
of flow is constant at 4,6 m/s. the guide vanes make an angle of 18 degrees with the tangent to the
rotor. There is no tapered draft tube. Determine

(a) The peripheral speed of the rotor as well as the exit angle of the rotor blades for maximum
power,

(b) What percentage of the available power is lost as kinetic energy at the exit?

Answers ( 26%, 14,2m/s, 4,9%)

5. An inward flow reaction turbine has a rotor of which the inside diameter is half of the outer
diameter. The velocity of flow is constant and equal to 0,16 where H is the available
3
pressure head . the flow rate is 0,3m /s due to an available head of 12m and the speed is 300r/min
. The inlet angle of the rotor blades is 90 degrees to the tangent to the rotor. The rotor blades
constitute 10% of the circumference of the rotor and the hydraulic efficiency is 0,8. Determine for
maximum power output,

(a) The guide vane angle

(b) The exit angle of the rotor blades

(c) The vertical height (breath) of the rotor blades at the inlet and the outlet.

Answers ( 14,2 degrees, 26,8 degrees, 70mm, 140 mm)

6. A Francis turbine must rotate at 150 r/min and deliver 160 kw when the available pressure head
is 12,5 m. the velocity of flow must be constant everywhere in the rotor at 0,251 . The
peripheral speed at inlet is 0,8 and the water must not have any whirl velocity component
at the exit from the rotor. Assume the hydraulic efficiency is 87% and the overall efficiency 79%.
Determine

(a) The diameter of the rotor

(b) The angle of the guide vanes,

(c) The angle of the inlet of the rotor blades,

(d) The breadth of the rotor blades at the inlet if the blades constitutes 8% of the circumference

Answers (1,615m, 25,1 degrees, 42,6 degrees, 90 mm)

7. The total pressure head in the spiral casing of a Francis turbine is 50m. the inner and outer
diameters of the rotor are 300 mm and 500 mm respectively, the rotor is 75 mm wide at the inlet,
the rotor inlet angles are 90 degrees in relation to the guide vanes and the exit angle of the guide
vanes is 25 degrees. water leaves the rotor blades radially at the same height as that of the incoming
water . the velocity of flow through the rotor is constant . the rotor blades take up to 8 % of the
circumference . take the losses in the guide vanes as 1, 2 m and the rotor 1,8 m of water and the
pressure at the exit of the rotor as atmospheric . calculate

(a) The rotational speed of the rotor

(b) the exit angles of the rotor blades

(c) The flow rate

(d) The power transferred to the rotor

(e) The pressure at the inlet to the rotor

Answers ( 867r/min, 32,5 degrees, 0,942 m3 /s, 399kw, 267 kpa

8. The shaft of a Francis turbine rotates at 300r/min.it delivers 3, 4 mw under an effective pressure
head of 47 m and the overall efficiency is then 81% and hydraulic efficiency 89% . the inlet to the
rotor is 1,55m above the tail race water level and the pressure head there is 26m. the suction pipe
inlet is 1,25 m above the tail race level and the pressure there is -2,3m. the turbine is operated for
maximum power . the water enters the draft tube at 6,1 m/s and leaves it at 3,5m/s. the outer
diameter of the rotor is 1,48 m and the velocity of flow is constant at 6,5 m/s. determine

(a) the power available power from the physical enviroment

(b) the flow rate

(c) the inlet angle of the rotor blades

(d) the exit diameter ofvthe draft tube

(e)the head losses in the guide vanes , the rotor and the draft tube.

answers( 4, 198mw, 9,105m3 /s, 49, 3 degrees, 1,82 m , 1,417 m, 2,906 m , 0,22 m)

9. The diameter of a pelton wheel is 0,9 m. The pressure head in front of the nozzle is 220m and
the nozzle has a velocity coefficient of 0,98. The exit angle of the buket is 18 degrees. Determine

(a) the best rotational speed

(B) the hydraulic efficiency of the turbine if the speed is 800r/ min

(c) the hydraulic efficiency of the wheel only, if the speed is 800r/min

answers(684r/min, 91%, 95%)

10. A pelton wheel has a diameter of 1,1 m and rotates at N rev/min.The velocity of the jet is 62m/s
and the relative velocity is 15% slower at the outlet from the buckets than at the inlet. The exit
angle of the buckets is 15 degrees. Derive from first principles an expression for the hydraulic
efficiency of the wheel. Plot a graph of the hydraulic efficiency versus speed for values of N of
400 up to 800r/min, and determine from the speed at which maximum efficiency occurs. Answer
(538r/min)
11. A pipeline 1800m long supplies water to a pelton wheel from a reservoir which is 400m higher
than the turbine. The turbine has two nozzles and develops 5000kw(mechanical) at 500r/min. The
pipeline losses are 10% of the gross head and the pipe friction coefficient f= 0,005.The nozzles
have Cv values of 0,98, the bucket speed is0,46of the jet velocity and the overall efficiency of the
turbine is 87%. Calculate the diameter of the pipe, the cross sectional area of the jets and the pitch
circle diameter of the buckets.

Answers (726 mm, 0,01m2 , 1,45m)

12. a test on a pelton turbine provided the following data: jet diameter 71mm, total pressure in
front of the nozzle1,18mpa, power output 198 kw, flow rate 0,188m3/s. calculate the available
power , the power loss in the nozzle and the overall efficiency of the turbine.

Answers ( 221,9kw,10kw, 89,2%)