# Soimilarity laws for turbines when efficiency are different

## Answers

**Explanation:**

When investigating flow phenomena, cost factors often favour the use of models which are geometrically similar to the original, full-sized equipment (see Similarity conditions). For this type of testing it is necessary that models are not only geometrically similar, but are also subjected to similar physical conditions.

The physical laws (differential equations including boundary conditions) applied must remain invariant under similarity transformations. This is achieved by dividing all relevant physical quantities by exponential products characteristic of the configuration to be tested so as to obtain ratios of the unit 1.

Physical similarity is achieved if the ratios (see Characteristic coefficient) of the original and the model are the same. The relationships established between the physical quantity of the original and that of the model by means of the characteristic coefficients are called affinity laws.

Using characteristic pump parameters such as the impeller diameter (D), rotational speed (n ), acceleration due to gravity (g) and the density of the fluid handled (ρ), various characteristic coefficients can be established for a centrifugal pump assuming frictionless, incompressible, non-cavitating flow.

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