Question

A Francis turbine has an overall efficiency of 83%. If it develops the power of 500 kW under a net head of 3000 cm, the discharge through the turbine in m³/s is:

1. 2.50
2. 20.50
3. 25.0
4. 2.05

Answer 1

Correct Answer - Option 4 : 2.05

CONCEPT:

The overall efficiency (η) of the reaction turbine is given by:

\(η = \frac{P_o}{P_i}\)

Where Po is the output power and Pi is input power.

The input power (p) is given by:

P = ρ g Q h

Where ρ is density, g is the acceleration due to gravity, Q is discharged, and h is the net head.

Calculation:

Given:

Density of water (ρ) = 1000 kg/m3

Net head (h) = 3000 cm = 30 m

Output power P_o = 500 kW

η = 83% = 0.83

Acceleration due to gravity (g) = 9.8 m/s2

Discharge (Q) = ?

Input power (Pi) = ρ g Q h = 1000 × 9.8 × Q × 30 = 294Q × 10³ 

Efficiency, \(η = \frac{P_o}{P_i}\) 

\(0.83 = \frac{500~\times~ 10^3}{294Q~\times ~10^3}\)

discharge, Q = 2.05 m³/s