Question

A hydraulic turbine develops 8000 kW when running at 300 rpm under a head of 45 m. the speed of the same turbine under a head of 60 m is
1. 224.4 rpm
2. 346.4 rpm
3. 424.8 rpm
4. 485.8 rpm

Answer 1

Correct Answer - Option 1 : 224.4 rpm

Concept:

The specific speed of a turbine is defined as, the speed of a geometrically similar Turbine that would develop unit power when working under a unit head (1 m head). Is prescribed by the relation.  \({N_s} = \frac{{N\sqrt P }}{{{H^{\frac{5}{4}}}}}\)

Calculation:

By specific speed, we understand the speed of geometrically similar turbines which would develop 1 kW power when operated under 1 m head.

P = 8000 kW

N₁ = 300 rpm

H₁ = 45 m

\({N_s} = \frac{{N\sqrt P }}{{{H^{\frac{5}{4}}}}}\)

For the same power, \({N} \propto \frac{1}{{{H^{\frac{5}{4}}}}}\)

\(\begin{array}{l} {N_2} = {N_1}{\left( {\frac{{{H_1}}}{{{H_2}}}} \right)^{\frac{5}{4}}}\\ = 300 \times {\left( {\frac{{45}}{{60}}} \right)^{\frac{5}{4}}} \end{array}\)

⇒ 209.4 rpm

∴ Option 1 is more appropriate.