Page 325 - Fluid Mechanics and Thermodynamics of Turbomachinery

306 Fluid Mechanics, Thermodynamics of Turbomachinery
Yedidiah, S. (1981). The meaning and application-limits of Thoma’s cavitation number. In
Cavitation and Polyphase Flow Forum 1981 (J. W. Hoyt, ed.) pp. 45 6, Am. Soc. Mech.
Engrs.
Young, F.R. (1989). Cavitation. McGraw-Hill.

Problems

1. A generator is driven by a small, single-jet Pelton turbine designed to have a power
specific speed  SP D 0.20. The effective head at nozzle inlet is 120 m and the nozzle velocity
coefficient is 0.985. The runner rotates at 880 rev/min, the turbine overall efficiency is 88 per
cent and the mechanical efficiency is 96 per cent.
If the blade speed to jet speed ratio, D 0.47, determine:
(1) the shaft power output of the turbine;
(2) the volume flow rate;
(3) the ratio of the wheel diameter to jet diameter.
2. (a) Water is to be supplied to the Pelton wheel of a hydroelectric power plant by a pipe
of uniform diameter, 400 m long, from a reservoir whose surface is 200 m vertically above
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the nozzles. The required volume flow of water to the Pelton wheel is 30 m /s. If the pipe
skin friction loss is not to exceed 10% of the available head and f D 0.0075, determine the
minimum pipe diameter.
(b) You are required to select a suitable pipe diameter from the available range of stock
sizes to satisfy the criteria given. The range of diameters (m) available are: 1.6, 1.8, 2.0, 2.2,
2.4, 2.6, 2.8. For the diameter you have selected, determine:

(1) the friction head loss in the pipe;
(2) the nozzle exit velocity assuming no friction losses occur in the nozzle and the water
leaves the nozzle at atmospheric pressure;
(3) the total power developed by the turbine assuming that its efficiency is 75% based upon
the energy available at turbine inlet.

3. A multi-jet Pelton turbine with a wheel 1.47 m diameter, operates under an effective
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head of 200 m at nozzle inlet and uses 4 m /s of water. Tests have proved that the wheel
efficiency is 88 per cent and the velocity coefficient of each nozzle is 0.99.
Assuming that the turbine operates at a blade speed to jet speed ratio of 0.47, determine:

(1) the wheel rotational speed;
(2) the power output and the power specific speed;
(3) the bucket friction coefficient given that the relative flow is deflected 165 ° ;
(4) the required number of nozzles if the ratio of the jet diameter to mean diameter of the
wheel is limited to a maximum value of 0.113.
4. A four-jet Pelton turbine is supplied by a reservoir whose surface is at an elevation of
500 m above the nozzles of the turbine. The water flows through a single pipe 600 m long,
0.75 m diameter, with a friction coefficient f D 0.0075. Each nozzle provides a jet 75 mm
diameter and the nozzle velocity coefficient K N D 0.98. The jets impinge on the buckets of
the wheel at a radius of 0.65 m and are deflected (relative to the wheel) through an angle
of 160 deg. Fluid friction within the buckets reduces the relative velocity by 15 per cent.
The blade speed to jet speed ratio, D 0.48 and the mechanical efficiency of the turbine is
98 per cent.