Question

A model of a hydraulic turbine is tested at a head of 1/4^th of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If N is the RPM of the full scale turbine, then the RPM of the model will be
1. N/4
2. N/2
3. N
4. 2N

Answer 1

Correct Answer - Option 3 : N

From similitude

\({\left( {\frac{{gH}}{{{N^2}{D^2}}}} \right)_{Model}} = {\left( {\frac{{gH}}{{{N^2}{D^2}}}} \right)_{actual}}\)

∴ Given H_model = H/4

D_model = D/2

\(\Rightarrow \frac{{\frac{{gH}}{4}}}{{N_{model}^2{{\left( {\frac{D}{2}} \right)}^2}}} = \frac{{gH}}{{{N^2}{D^2}}} \Rightarrow {N_{actual}} = {N_{model}}\)