The pressure rise across a pump P (this term is proportional to the head developed by the pump) may be considered to be affected by the fluid density , the angular velocity , the impeller diameter D,...

The pressure rise across a pump P (this term is proportional to the head developed by the pump) may be considered to be affected by the fluid density
, the angular velocity
, the impeller diameter D, the volumetric rate of flow Q, and the fluid viscosity
. Find the pertinent dimensionless groups, choosing them so that P, Q, and m each appear in one group only. Find similar expressions, replacing the pressure rise first by the power input to the pump, then by the efficiency of the pump.