Similarity and Dimensional Analysis

Thus, represents the condition for kinematic similarity, and is known as capacity coefficient or discharge coefficient The second term is known as the head coefficient since it expresses the head H in dimensionless form. Considering the fact that ND rotor velocity, the term becomes , and can be interpreted as the ratio of fluid head to kinetic energy of the rotor, Dividing by the square of we get

The term can be expressed as and thus represents the Reynolds number with rotor velocity as the characteristic velocity. Again, if we make the product of and , it becomes which represents the Reynolds's number based on fluid velocity. Therefore, if is kept same to obtain kinematic similarity, becomes proportional to the Reynolds number based on fluid velocity.

The term expresses the power P in dimensionless form and is therefore known as power coefficient . Combination of and in the form of gives . The term 'PQgH' represents the rate of total energy given up by the fluid, in case of turbine, and gained by the fluid in case of pump or compressor. Since P is the power transferred to or from the rotor. Therefore becomes the hydraulic efficiency for a turbine and for a pump or a compressor. From the fifth term, we get

Multiplying , on both sides, we get

Therefore, we find that represents the well known Mach number , Ma.

For a fluid machine, handling incompressible fluid, the term can be dropped. The effect of liquid viscosity on the performance of fluid machines is neglected or regarded as secondary, (which is often sufficiently true for certain cases or over a limited range).Therefore the term can also be dropped.The general relationship between the different dimensionless variables ( terms) can be expressed as

	(3.1)

Therefore one set of relationship or curves of the terms would be sufficient to describe the performance of all the members of one series.