Question

A Pelton wheel with a single jet rotates at 300 rpm. The velocity of the jet from the nozzle is 100 m/s. If the ratio of the vane velocity to jet velocity is 0.44, what is the diameter of the Pelton wheel? 
1. 2.8 m
2. 1.4 m
3. 0.7 m
4. 2.1 m

Answer 1

Correct Answer - Option 1 : 2.8 m

Concept:

Design parameters of Pelton wheel turbine:

1. Velocity of jet: at the inlet \({V_1} = {C_V}\sqrt {2gH} \) where C_v = coefficient of velocity = 0.98-0.99

2. Velocity of wheel: \(u = \emptyset \sqrt {2gH} \) where φ is the speed ratio = 0.43-0.48

3. Pitch or mean diameter: D can be expressed by \(u = \frac{{\pi DN}}{{60}}\)

Calculation:

Given,

N = 300 rpm, V = 100 m/s

The ratio of the vane velocity to jet velocity = 0.44

\(\begin{array}{l} \frac{u}{v} = 0.44\; \to \;\frac{u}{{100}} = 0.44\; \to u = 44\ \frac{m}{s}\\ u = \;\frac{{\pi DN}}{{60}}\; \to 44 = \;\frac{{\pi *D*300}}{{60}}\; \to D = 2.8\ m \end{array}\)