In these turbines, a high-speed jet at a velocity of Vjet impinges on buckets, forcing the wheel to
rotate. The buckets reverse the direction of the jet, and the jet leaves the bucket making an angle
β with the direction of the jet, as shown in the figure.
1. Show that the power produced by a Pelton wheel of radius r rotating steadily at an angular
velocity of ω is
( )(1 cos ) W r shaft j = Q V r − −
where ρ is the fluid density and Q is the volume flow rate of the fluid.
2. Obtain the numerical value of the power for ρ = 1000 kg/m3
, r = 2 m, Q=10 m3
/s, N = 150
rpm, β = 160°, and Vjet = 50 m/s.
3. Investigate the effect of the angle 𝛽 on the power generation by allowing it to vary from 0° to
180°. Plot the power produced versus the angle 𝛽. Use conditions given in point 2 above.
4. Is it practical to use 𝛽 = 180° to maximize the turbine power? identify the best range of
bucket angle 𝛽.
5. Investigate the effects of jet velocity on the turbine power.
6. Investigate the effects of wheel diameter on the turbine power.
7. Recommend ways to optimize the turbine performance.
Report to include:
1. cover page
2. Abstract
3. Introduction on Pelton wheel Turbine, and how it works
4. Theoretical background: governing equations, control volumes, simplifications,
assumptions, and detailed analysis of power generation
5. Results and discussion: show plots of variations and discuss values and trends.
6. Conclusions and recommendations