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A turbine develops 500 kW power under a head of 100 in at 200 rpm. What would be its normal speed under a head of 81 m? 
1. 250 rpm
2. 550 rpm
3. 180 rpm
4. 670 rpm
5. 900 rpm

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Correct Answer - Option 3 : 180 rpm

Concept:

Unit speed i.e. speed of the turbine under unit head,

\({{\rm{N}}_{\rm{a}}} = \frac{{\rm{N}}}{{\sqrt {\rm{H}} }}\)

Given: P = 500 kW, H1 = 100 m, N1 = 200 rpm, and H2 = 81 m

To Calculate: N2 = ?

Calculation:

\(\frac{{{{\rm{N}}_1}}}{{\sqrt {{{\rm{H}}_1}} }} = \frac{{{{\rm{N}}_2}}}{{\sqrt {{{\rm{H}}_2}} }} \Rightarrow \frac{{200}}{{\sqrt {100} }} = \frac{{{{\rm{N}}_2}}}{{\sqrt {81} }}\)

\(\Rightarrow {{\rm{N}}_2} = \frac{{20 \times 9}}{{10}} = 180{\rm{\;rpm}}\)

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