# A turbine develops 8000 kW when running at 1000 rpm. The head on the turbines is 30 m. If the head is reduced to 18 m, what is the speed developed by

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A turbine develops 8000 kW when running at 1000 rpm. The head on the turbines is 30 m. If the head is reduced to 18 m, what is the speed developed by the turbine?
1. 67.46 rpm
2. 95.24 rpm
3. 54.67 rpm
4. 774.6 rpm
5.

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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