The affinity law of pump

The actual performance characteristics curves of pumps have to be determined by experimental testing. The affinity laws are derived from a dimensionless analysis of three important parameters that describe pump performance: flow, total head and power. The analysis is based on the reduced impeller being geometrically similar and operated at dynamically similar conditions or equal specific speed. If that is the case then the affinity laws can be used to predict the performance of the pump at different diameters for the same speed or different speed for the same diameter.

The affinity laws of centrifugal pump performance express the effect on pump performance due to changes in certain application variables. The affinity law variables which affect pump performance are:

1) Pump speed(N) in pump revolutions per minute (RPM).

2) Impeller diameter(D).

If, Pump speed-N(rpm) is constant,

If pump with a constant speed(N), the capacity will be directly proportional to the impeller diameter, the head will be directly proportional to the square of the impeller diameter, and the required power will be directly proportional to the cube of the impeller diameter.

Q2 = Q1 (D2/D1), H2 = H1 Sqr of (D2/D1) P2 = P1 Cubic of (D2/D1)

where,

Q2 = New capacity (Flow rate)

Q1 = Initial capacity (Flow rate)

H2 = New Head in mtr

H1 = Initial Head in mtr

D2 = New Diameter of impeller

D1 = Initial Diameter of impeller

P2 = New Power in KW

P1 = Initial Power in KW

If, Pump Impeller Diameter-D is constant,

If pump with a fixed diameter impeller(D), the capacity will be directly proportional to the speed, the head will be directly proportional to the square of the speed, and the required power will be directly proportional to the cube of the speed.

Q2 = Q1 (N2/N1), H2 = H1 Sqr of (N2/N1) P2 = P1 Cubic of (N2/N1)

where,

Q2 = New capacity (Flow rate)

Q1 = Initial capacity (Flow rate)

H2 = New Head in mtr

H1 = Initial Head in mtr

N2 = New speed of pump in rpm

N1 = Initial speed of pump in rpm

P2 = New Power in KW

P1 = Initial Power in KW

If Diameter-D and Pump speed-N(rpm) change,

Q2 = Q1 (D2/D1 x N2/N1)

H2 = H1 Sqr of (D2/D1 x N2/N1) 

P2 = P1 Cubic of (D2/D1 x N2/N1)

where,

Q2 = New capacity (Flow rate)

Q1 = Initial capacity (Flow rate)

H2 = New Head in mtr

H1 = Initial Head in mtr

N2 = New speed of pump in rpm

N1 = Initial speed of pump in rpm

P2 = New Power in KW

P1 = Initial Power in KW

D2 = New Diameter of impeller

D1 = Initial Diameter of impeller