by Terry Henshaw

The concept of “suction energy” was developed to enhance the evaluation of the NPSH characteristics of centrifugal pumps, but I fear that it misses the mark. Suction energy is defined as the product of U1 (the peripheral velocity of the impeller eye) and S (suction specific speed). At first blush, that seems like a reasonable concept, but a mathematical analysis seems to indicate a flaw in the logic. The equation for suction energy is:


Es = U1 x S                                                               (1)


Es = suction energy

U1 = peripheral velocity of impeller eye, ft./sec.

S = suction specific speed (rpm-gpm-ft.)


The equation for S, suction specific speed, is:

S =       N√Q / (NPSHr)0.75                                       (2)



N = rotative speed of impeller, rev./min.

Q = capacity of one eye at best-efficiency-point, US gal./min.

NPSHr = net positive suction head, normally at 3 percent head drop (of first stage), feet

Using the “Classic” Relation Between NPSHr And U1

As shown in Reference 1, at no-prerotation capacity (which is at, or near, the best efficiency point—BEP), NPSHr can be expressed by the following equation:

NPSHr = U12/2g  [(K1 + K2) tan2 β1 + K2]                   (3)


g = gravitational constant, 32.2 ft./sec.2

K1 and K2 = experimental constants, established by test

β1 = inlet vane angle, normally measured at the shroud, degrees

Everything on the right side of Equation 3 can be considered constant, except for U1. We can, therefore, say that:

NPSHr = K3U12                                                        (4)

Solving for U1:

U1 = [NPSHr/K3]0.5                                                  (5)


If we plug Equations 2 and 5 into Equation 1, we get:

Es = U1 x S = [NPSHr/K3 ]0.5[ N√Q / (NPSHr)0.75]      (6)

But wait a minute. We have (NPSHr)0.5 in the numerator, multiplied by (NPSHr)0.75 in the denominator. Don’t those tend to cancel each other? Yes, they do. The resulting equation is:

Es = [ 1/K3]0.5[ N√Q / (NPSHr)0.25]                          (7)

The effect of NPSH on the characteristic has been significantly reduced, with the exponent dropping from 0.75 to 0.25, a two-thirds reduction. We’ve almost eliminated NPSH from the equation, and that should not happen. NPSH is what it is all about.

If we envision suction specific speed as a stool supported by three legs, with each leg being (NPSHr)0.25, then multiplying by U1 cuts off two of the legs.

I prefer to sit on a stool that has three legs.