What is a pump flow coefficient and what is it used for?

The flow coefficient characterizes the capacity of a pump under certain operating conditions based on similarity considerations. It is a dimensionless coefficient which is constant for all capacities considering similar flow conditions. Conversely, the capacity for a geometrically similar pump can be determined, in order to achieve similar flow conditions.

From the philosophy of the similarity considerations it follows that flow similarity in hydrodynamic machines is achieved, when the ratio between the local fluid velocity and the circumferential velocity of the rotor at all considered geometrically similar locations of the machines is constant. The (local) fluid velocity is denoted by v and the circumferential velocity is denoted by u.

v is proportional to capacity (volume flow rate) Q divided by the characteristic length, the diameter of the rotor, Dsquared. Furthermore, u is proportional to the rotational speed U multiplied with the rotor diameter. The previously established relation is therefore rewritten.

ϕ is referred to as the flow coefficient and is constant at similar flow conditions. This condition is satisfied if the rotational speed and capacity of a pump are changed proportionally to one another. Additionally, the flow coefficient may be used in order to compare two geometrically similar pumps to one another with a varying rotor diameter, to determine the operating conditions (Q, N) in order to obtain similar flow conditions.