Q on Pumps (esp. 4 ME's)

Factual Questions
1

Anyone heard of affinity laws or affinity equations regarding a pump’s behavior? My Eastern European fluds prof. failed to make mention of such terms…we just applied “this” or “that” without an appreciation for the background - which is important, as well!
Thanks,

  • Jinx
2

Do you mean akin to fan laws? :confused:

3

From “Cameron Hydraulic Data” (aside: this is a great reference for MEs - most college texts are crap, but every ME should own Cameron Hydraulic and Crane technical Paper 410):

For pumps in the centrifugal range of specific speeds (radial flow impellers) the relationship between capacity, head and horsepower with changes in impeller diameter are approximately as follows:

For small variations in impeller diameter (constant speed):

D1/D2 = Q1/Q2 = SQRT(H1)/SQRT(H2)

BHP1/BHP2 = (D1)^^3/(D2)^^3 <–(That’s cubed; I don’t know how to do superscripts here)

For variations in speed (constant impeller diameter):

S1/S2 = Q1/Q2 = SQRT(H1)/SQRT(H2)

BHP1/BHP2 = (S1)^^3/(S2)^^3

where:
D = Impeller diameters in inches
H = Heads in feet
Q = Capacities in gpm
S = Speeds in rpm
BHP = Brake Horsepowers

Note: Subscript 1 is for original design conditions.

The above relationships are known as the AFFINITY LAWS and are offered in this text with the understanding their application will be limited to centrifugal (radial flow) type pumps only. When other types such as axial flow, mixed flow or propeller type are involved consult the manufacturer for instructions.

These laws can be summarized as follows:

With variable speeds the capacity varies directly and the head varies with the square of the speed; efficiencies will not change for reasonable variations in speed. The brake horsepower (BHP) varies as the cube of the speed.

With variable impeller diameters the capacity varies directly and the head varies as the square of the impeller diameter - efficiency will be reduced as the diameter is reduced - check manufacturer for limitations. The brake horsepower varies as the cube of the impeller diameters. Note: These relations hold only for small changes in impeller diameter.