ASSIGNMENT-01
1. A pelton wheel having semi-circular buckets functions under a head of 150 m and
consumes 50 liter per second of water. If 60 cm diameter wheel turns 600 revolutions
per minute, make calculations for the power available at the nozzle and the hydraulic
efficiency of the wheel. Presume coefficient of velocity kv is unity and friction factor
at bucket as 0.95. [73575 W, 0.884]
2. A Pelton wheel has a mean bucket speed of 12 m/s and is supplied with water at the
rate of 750 lit/s under a head of 35 m. If the buckets deflect the jet through an angle
160º, find the power and the efficiency of the turbine neglecting friction in bucket. Take
the coefficient of velocity as 0.98. [238.83 kW, 0.927]
3. In a hydroelectric power plant, water available under a head of 250 m is delivered to
the power house through three pipes having 2500 m length. Through these pipes,
friction loss is estimated to be 20 m. The project is required to produce a total shaft
output of 13.25 MW by installing a number of single jet Pelton wheels whose specific
speed is not exceeding 38.5. It is given as wheel speed is 650 rpm, ratio of bucket to jet
speed is 0.46, overall efficiency of the wheel is 85 %, nozzle Cd is 0.94 and kv is 0.97.
Pipe friction coefficient is also given as 0.005. Determine (i) the number of Pelton
wheel to be used (ii) jet diameter (iii) diameter of the supply pipes. [5, 0.167 m, 0.274m]
4. An inward flow reaction turbine works under a head of 30 m and discharge of 10 m3/s.
The speed of the runner is 300 r.p.m. At the inlet tip of the runner vane the peripheral
velocity of wheel is 0.9√(2gh) and the radial velocity of flow is 0.3√(2gh), where h is
the head on the turbine. If the overall efficiency and hydraulic efficiency of the turbine
are 80% and 90% respectively, determine (i) power developed in kW (ii) diameter and
width of the runner at inlet and (iii) guide blade angle at inlet (iv) Inlet angle at runner
vane β1. Assume blade thickness coefficient as 0.95. [2354.4 kW, D=1.39 m, b=0.331
m, 30.78o, 143.12o]
5. An inward flow reaction turbine with a supply of 550 lit/sec under a head of 15 m
develops 74.6 kW at 400 rpm. The inner and the outer diameter of the runner are 50 cm
and 75 cm respectively. The velocity of water at exit is 3 m/s assuming that the
discharge is radial and that the width of the wheel is constant, find the overall and the
theoretical hydraulic efficiencies of the turbine and the inlet angles of the guide and
wheel vanes. [ 92.2%, 97.9%, 14.3o, 10.3o]
6. A Kaplan turbine with runner diameter 4 m, the discharge is 60 m3/s and hydraulic and
mechanical efficiencies are stated to be 90% and 94% respectively. The diameter of
boss is 0.1 times the runner diameter and the speed ratio is 0.9. Assuming that discharge
is free and there is no swirl at outlet; calculate (i) the net available head on the turbine
(ii) the power developed and (iii) specific speed. [ 11.9 m, 5905.7 kW, 228.92]
7. A small hydro development, a Kaplan turbine runs under a head of 2.1m. It has a runner
of 3.5 m diameter and develops 600 kW at 80 r.p.m. Determine the discharge and
specific speed of the machine assuming an overall efficiency of 80%. If a homogeneous
turbine is to be tested at a head of 3.0 m and diameter 1.5 m, what are the rotational
speed, discharge and power of the unit? [36.41 m3/s, Ns=775.16 and Nm=386.44
Qm=0.51 m3/s, Pm= 4.0 kW]
8. In a hydroelectric power plant 12 MW is required. A Kaplan turbine develops works at
195 rpm under 12 m head and with an overall efficiency of 85 percent. The geometric
and flow parameters are as follows: speed ratio (based on outer diameter) is 2.0, flow
ratio is 0.63, and diameter of the boss is 35 percent of external diameter of the runner.
Find the specific speed of the turbine and number of turbines needed to fulfill the power
requirement. [677.6, 2]