What are similarity considerations and what is their use?

Similarity considerations are used to compare the hydraulic performance of a hydrodynamic machine with the hydraulic performance of another, considering geometrically similar flow paths. Even when operating conditions differ, comparison of various pumps (sizes) is possible. Similarity considerations may also be used to compare various operating conditions of one machine, while maintaining geometrically similar flow conditions. Similarity considerations are only valid for incompressible flows, i.e. the mass density of the fluid is constant.

Flow conditions between multiple systems are considered geometrically similar when all fluid velocities are varied with the same ratio at all considered geometrically similar locations between the considered systems. Examples of geometrically similar locations are the tip of the impeller, the inlet of an impeller, the outlet of a volute etc. The flow coefficient, head coefficient and power coefficient are a product of these considerations and are referred to as similarity relations. They completely describe the performance of a hydrodynamic machine, along with the hydraulic efficiency. Expressing performance characteristics in a dimensionless fashion yields equal performance curves for any other geometrically similar pump with a varying rotor diameter or any other combination of the power P, the rotational speed N, the capacity Q or the generated head H. Note that these similarity relations do not hold for unsteady flows, or cavitating flows.