# Pelton wheel's theoretical speed for max efficiency

1. Jul 21, 2013

### Michael V

1. The problem statement, all variables and given/known data

A Pelton wheel is driven by five identical jets. The runner has a diameter of 3,8 m, fixed in a horizontal position. The head from reservoir level to nozzles is 350 m and the efficiency of power transmission through the pipeline and nozzles is 90%. The relative velocity decreases by 8% as the water traverses the bucket surfaces which deflect the jet at an angle of 162°. The coefficient of velocity for the jets is 0,97 (Cv) and the discharge is 25920 m$^{3}$/hour.
Calculate the following:
a) The velocity of water entering the buckets
b) The theoretical wheel speed in r/min for maximum efficiency (u = 0,5 V)

2. Relevant equations

For a: $V = Cv\sqrt{2g×h}$ where h = Height×90%

For b: $U = \frac{\pi×D×N}{60}$

3. The attempt at a solution

a) $V = Cv\sqrt{2g×h} = 0,97×\sqrt{2(9,81)×315} = 76,256 m/s$

b) $U = 0.5V = \frac{\pi×D×N}{60}$
I'm confused as to whether I must use V from (a) or if I must calc a new V where h = H for max efficiency?

Last edited: Jul 21, 2013