GATE 2021 ME (ME1) – Question 58
A single jet Pelton wheel operates at 300 rpm. The mean diameter of the wheel is 2 m. Operating head and dimensions of jet are such that water comes out of the jet with a velocity of 40 m/s and flow rate of 5 m³/s. The jet is deflected by the bucket at an angle of 165°. Neglecting all losses, the power developed by the Pelton wheel is _____ MW (round off to two decimal places).
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Correct answer: 2.64 to 2.66
Explanation
Bucket speed is $u=\pi DN/60=31.4159$ m/s. Relative inlet speed is V−u=8.58407 m/s, unchanged in magnitude for a lossless bucket.
Tangential momentum change per unit mass is $(V-u)(1+\cos15^\circ)$. Thus $P=\rho Q u(V-u)(1+\cos15^\circ)=\mathbf{2.65}$ MW, using water density 1000 kg/m³.