Question

A Pelton wheel develops 1750 kW under a head of 100 m while running at 200 rpm and discharging 2500 litres of water per sec. The unit power of the wheel will be

1. 3.75 kW
2. 0.75 kW
3. 1.75 kW
4. 0.25 kW

Answer 1

Correct Answer - Option 3 : 1.75 kW

Concept:

The power developed by a turbine, working under a unit head is known as the unit power of the turbine.

P = ρgQH

P ∝ QH

Now,

Q = AV

V ∝ H^1/2

∴ Q ∝ H^1/2

Now,

P ∝ QH

P ∝ H^3/2

P = K₂H^3/2

When H = 1; P = P_u

P_u = K₂

P = P_uH^3/2

\({{\bf{P}}_{\bf{u}}} = \frac{{\bf{P}}}{{{{\bf{H}}^{\frac{3}{2}}}}}\)

Calculation:

Given:

P = 1750 kW, H = 100 m

\({{\rm{P}}_{\rm{u}}} = \frac{{\rm{P}}}{{{{\rm{H}}^{\frac{3}{2}}}}} = \frac{{1750}}{{{{\left( {100} \right)}^{\frac{3}{2}}}}} = 1.75{\rm{\;kW}}\)

∴ the unit power of the wheel is 1.75 kW.