A pump, before it is sent for manufacturing should be tested for any faults in design and operation. It would be wasteful to make a full-sized product for testing purposes.

Hence, a scaled down model, identical to the actual prototype is created with scaled down dimensions. The similarity relations have the following assumptions:

i) Velocities are a function of monometric head.

ii) The pumps have proportionate impeller diameter and are geometrically similar.

iii) They have similar hydraulic and volumetric efficiencies.

The following parameters need to be satisfied for the model and prototypes to be similar:

i)Equal specific speeds

${N_{sm}}={N_{sp}}$

$\frac{{N_m}{\sqrt{Q_m}}}{H_m^{\frac{3}{4}}}=\frac{{N_p}{\sqrt{Q_p}}}{H_p^{\frac{3}{4}}}$

ii)Head coefficients are equal

$\frac{H}{D^2N^2}=constant$

$\frac{H_m}{D_m^2N_m^2}=\frac{H_p}{D_p^2N_p^2}$

iii) Discharge coefficients are equal

$\frac{Q}{D^3N}=constant$

$\frac{Q_m}{D_m^3N_m}=\frac{Q_p}{D_p^3N_p}$

iv) Power coefficients are equal

$\frac{P}{D^5N^3}=constant$

$\frac{P_m}{D_m^5N_m^3}=\frac{P_p}{D_p^5N_p^3}$