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

\(\frac{N_1}{{{\sqrt{H_1}}}}=\frac{N_2}{{{\sqrt{H_2}}}}\)

\(\frac{1000}{{{\sqrt{30}}}}=\frac{N_2}{{{\sqrt{18}}}}\)

N_{2} = 774.6 rpm