1. Design a pelton wheel for following data:
Power p = 12000 kw
Head H = 400m
Speed N = 700 rpm
ηo = 85%
Jet ratio = 6
Speed ratio = 0.45
Cv = 0.98
Find wheel diameter, number of jets, diameter of each jet.
Answer:
D = 1.1m no. of. jets = 4, d = 12cm
2. Pelton wheel works under a head of 400m. It is supplied with water by penstock of dia 1m and length 5km, and its friction factor 0.032. Jet of 15cm dia. Strikes the buckets and gets deflected through 165°, If Vr2 = 0.85, Vr1 = speed ratio 0.45 and ηm = 0.85, find:
1) Power developed by runner
2) Shaft power
3) ηh and ηo
Answer:
(1) 5028 kw;
(2) 4274 kw;
(3) ηh = 0.9, ηo = 0.76
3. Shaft power developed by a pelton wheel is 15400kw. Three jets each of 16cm dia. Strike the buckets under a head of 400m and get deflected through 160°. If Cv = 0.99, Ku = 0.45, find overall efficiency, hydraulic efficiency and mechanical efficiency.
Answer:
ηo = ηh = 0.96, ηm = 0.77
4. A pelton wheel has a nozzle diameter of 16cm and head available at nozzle is 400m. If Cv = 0.98, wheel diameter 1.75 m, jet gets deflected through 150° and wheel to jet speed ratio 0.46, find power developed by turbine, its speed and hydraulic efficiency.
Answer:
6065 kw, 436 rpm, 89%
5. A pelton wheel having a mean bucket diameter of 1.0m is running at 1000 rpm. The net head on the pelton wheel is 700m. If the side clearance angle is 15o and discharge through the nozzle is 0.1 m3/s, determine power available at the nozzle and hydraulic efficiency of the turbine.
Answer:
686.5 kw, 97.18%
6. The shaft power of a pelton wheel, the buckets of which are struck by two jets, is 15445 kw. The diameter of each jet is 200mm. If the net head on the turbine is 400m, find the overall efficiency of the turbine. Take Cv = 1.0
Answer:
70.8%
7. The jet of water coming out of nozzle strikes the buckets of a pelton wheel which when stationary would deflects the jet through 165°. The velocity of water at exit is 0.9 times at the inlet and the bucket speed is 0.45 times the jet speed. If the speed of the pelton wheel is 300rpm and the effective head is 150m, determine
(i) Hydraulic efficiency and (ii) Diameter of the pelton wheel,
Take co-efficient of velocity, Cv = 0.98
Answer:
(i) 92.5%
(ii) 1.55 m
8. The following data is related to a pelton turbine:
Brake/shaft power = 126.5 kw
Head = 300m
Speed = 600 rpm coefficient of velocity, Cv = 0.98
Speed ratio, Ku = 0.45
Overall efficiency, η。 = 75%
Determine the following.
(i) The discharge
(ii) The least jet diameter,
(iii) The mean runner diameter jet ratio, and
(iv) The number of buckets,
Answer:
(i) 0.0573 m3/s, (ii) 31mm, (iii) 35.6, (iv) 33
9. A pelton wheel has a mean bucket speed of 12m/s and is supplied with water at the rate of 0.7m3/s under a head of 30m. If the bucket deflect the jet through an angle of 160°, find the power and the efficiency of the turbine.
Answer:
194.12 kw; 93.4%
10. A peton wheel has to develop 13230 kw under a net head of 800m while running at a speed of 600 rpm. If the coefficient of the jet Cv = 0.97, speed ratio Ku 0.46 and the ratio of jet diameter is 1/16 of wheel diameter, determine the following:
(i) The diameter of the pitch circle
(ii) The diameter of each jet
(iii) The quantity of water supplied to the wheel and
(iv) The number of jets required
Assume overall efficiency as 85 percent.
Answer:
1.834m, 114.6 mm; 1.254 m3/s, 2
11. An inward flow reaction turbine has peripheral velocity of 24m/s at inlet. The axial and whirl velocity components at inlet are 2m/s and 8 m/s. The passage width and flow after at inlet are 150mm an 0.4m2, discharge is radial, ηh = 80%. Find wheel diameter at inlet and outlet, power developed, impressed head, rotational speed and blade angle at inlet and outlet.
Assume D2 = 0.5 D1 and velocity of flow constant.
Answer:
D1 = 0.85m, D2 = 0.425m, p = 345 kw, H = 55m, N = 540 rpm,
θ = 18.43°, ϕ = 9.46°
12. An inward flow reaction turbine has ηo = 80% and develops 136 kw. Head is 16m and ku = 0.75, flow ratio 0.25, N = 120 rpm and hydraulic losses, are 15% of a available energy. Find
(a) Wheel diameter
(b) discharge through turbine
(c) Guide blade angle
(d) runnet blade angle θ
Answer:
(a) D = 2.1m
(b) Q = 1.08m3/s
(c) d = 23.5°
(d) θ = 55°
13. An inward flow francis turbine develops 735 kw at 750 rpm under a head of 100m. The guide vane angle at inlet is 15°, breath ratio = 0.1, D2 = D1/2, velocity of flow is constant and discharge is radial. The runner blade thickness block 5% of flow area at inlet ηo = 84% find wheel diameter, wheel width at inlet, runner blade angle at inlet and outlet.
Answer:
D1 = 0.574 m, B1 = 5.74cm, θ = 38.78° ϕ = 24°
14. An inward flow Francis turbine has outer and inner diameters as 60cm and 40cm width a 5cm width at inlet. The wheel blade angles are 90° and 14°, velocity of flow is constant and 8% blockage of flow area due to blade thickness. If H = 54cm, ηh = 81% and discharge at exit radial, find
(a) Rpm of wheel
(b) power developed by runner
Answer:
N = 692 rpm, p = 128 kw
15. A Kaplan turbine produces 44000 kw under a head of 24.7m, with an overall efficiency of 90%. Taking the value of speed ratio as 1.6, flow ratio as 0.5 and hub diameter as 0.35 times the outside diameter, find the runner diameter and speed of the turbine.
Answer:
Do = 5.16m, N = 130.7 rpm
16. The following data pertain to a Kaplan turbine: shaft power = 13230kw; speed = 75 rpm: Head = 8m Diameter of boss of runner = 0.35 times the external diameter, speed ratio = 2. Flow ratio = 0.6 find the efficiency of the turbine,
Answer:
80.7%
17. A francis turbine with an overall efficiency of 75% is required to produce 149.26kw. It is working under a head of 7.62m. The peripheral velocity = 0.26 √2gH and the radial velocity of flow at inlet is 0.96 √2gH. The wheel runs at 150 rpm and hydraulic losses in the turbine are 22% of the available energy. Assuming radial discharge, determine
(i) The guide blade angle
(ii) The wheel vane angle at inlet
(iii) Diameter of wheel at inlet,
(iv) Width of wheel at inlet
Answer:
(i) α = 32.6°
(ii) θ = 37.7°
(iii) D1 = 0.404m
(iv) B1 = 0.17m
18. Calculate the efficiency of Kaplan turbine developing 2900 kw under a head of 5m. It is provided with a draft tube with its inlet (diameter 3m) set 1.6m above the tail race level. A vacuum gauge connected to the draft tube indicates a reading of 5m of water. Assume draft tube efficiency a) 78%
Answer:
ηo = 90.4%
19. A Kaplan turbine develops 20,000 kw of head of 35m and 420 rpm outer rpm outer diameter = 2.5m and inner diameter = 0.85m. If ηh = 90% and ηo = 85% По find discharge guide vane angle, runner blade angle at inlet and specific speed.
Answer:
Q = 68.6 m3/s, α = 70.5°, θ = 17.7°, Ns = 698
20. A turbine develops 8000kw at 1000 rpm and under a head of 30m. If head is reduced to 18cm, find speed and power developed by the turbine.
Answer:
N = 77.5 rpm, p = 3710 kw
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