Correct Answer - Option 4 : 774.6 rpm
Concept:
Unit Quantities:
If the speed, discharge, and power developed by a turbine under a head are known, then by using unit quantities the speed, discharge, and power developed by the same turbine under a different head can be obtained easily. They are as follows:
\(N_u=\frac{N_1}{\sqrt{H_1}}=\frac{N_2}{\sqrt{H_2}}\)
\(Q_u=\frac{Q_1}{\sqrt{H_1}}=\frac{Q_2}{\sqrt{H_2}}\)
\(P_u=\frac{P_1}{{H_1^{3/2}}}=\frac{P_2}{{H_2}^{3/2}}\)
Calculation:
Given:
P1 = 8000 kW, N1 = 1000 rpm, H1 = 30 m, H2 = 18 m
\(\frac{N_1}{{{\sqrt{H_1}}}}=\frac{N_2}{{{\sqrt{H_2}}}}\)
\(\frac{1000}{{{\sqrt{30}}}}=\frac{N_2}{{{\sqrt{18}}}}\)
N2 = 774.6 rpm