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:
\(\frac{{{{\rm{N}}_1}}}{{\sqrt {{{\rm{H}}_1}} }} = \frac{{{{\rm{N}}_2}}}{{\sqrt {{{\rm{H}}_2}} }} \Rightarrow \frac{{200}}{{\sqrt {100} }} = \frac{{{{\rm{N}}_2}}}{{\sqrt {81} }}\)
\(\Rightarrow {{\rm{N}}_2} = \frac{{20 \times 9}}{{10}} = 180{\rm{\;rpm}}\)