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 RPM of the model will be
1. N/4
2. N/2
3. N
4. 2N

Answer 1

Correct Answer - Option 3 : N

Concept:

The relation between rpm (N), diameter (D) and head (H) is, \(\frac{\sqrt{H}}{DN}\)

Calculation:

Given:

H_m = \(\frac{1}{4}\)H_p, D_m = \(\frac{1}{2}\)D_p

\(\begin{array}{l} \frac{{\sqrt {{H_m}} }}{{{D_m}{N_m}}} = \frac{{\sqrt {{H_P}} }}{{{D_P}{N_P}}}\\ \Rightarrow {N_m} = {N_P}\left( {\frac{{{D_P}}}{{{D_m}}}} \right)\sqrt {\frac{{{H_m}}}{{{H_P}}}} \\ \therefore {N_m} = N \times 2\sqrt {\frac{1}{4}} = N \end{array}\)