Establish the effect of speed on discharge, head developed and power required by pump.

Question

Application of dimensional analysis technique to incompressible flow roto-dynamic machines gives following dimensionless ratios:

         Using them only:

         1. Show that

(i)   $\pi _{1}$ Represents condition of kinematic similarity

(ii)  $\pi _{3}$ represents condition of dynamic similarity.

2. Establish the expression of:

(i) Unit speed, unit discharge and unit power for the turbine

(ii) Specific speed for turbine and pump.

3.   Establish the effect of speed on discharge, head developed and power required by pump.