Hydraulic Machines MCQ with answer and solution

Concept

Unit power is the power developed by a turbine working under a unit head of 1 metre.

Formula

P_u = P / H^3/2

Step-by-step solution

1. Identify given values: Power developed, P = 1750 kW Head, H = 100 m Speed, N = 200 r.p.m Discharge, Q = 2500 litres/s = 2.5 m³/s 2. Use the unit power formula: P_u = P / H^3/2 3. Calculate H^3/2: H^3/2 = (100)^3/2 = (√100)³ = 10³ = 1000 4. Calculate unit power: P_u = 1750 / 1000 = 1.75 kW Answer: (C) 1.75 kW

Explanation

Unit power is defined as the power produced when the operating head is 1 m. Dividing the total power of 1750 kW by 100^3/2 gives 1.75 kW. The discharge and speed values are extra data not needed for this formula.

Why the other options are wrong

A: 0.25 kW is obtained from incorrect power or discharge calculations. B: 0.75 kW is an incorrect calculation. D: 3.75 kW is an incorrect value.

Shortcut

For H = 100 m, H^3/2 is always 1000. So just divide power by 1000: 1750 / 1000 = 1.75 kW.

Common mistake

Dividing power simply by H instead of H^3/2, or confusing unit power with unit discharge.