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:

E_{s} = U_{1} x S (1)

Where:

E_{s} = suction energy

U_{1} = 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)

Where:

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 = U_{1}^{2}/2g [(K_{1} + K_{2}) tan^{2} β_{1} + K_{2}] (3)

Where:

g = gravitational constant, 32.2 ft./sec.^{2}

K_{1} and K_{2} = experimental constants, established by test

β_{1} = 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 = K_{3}U_{1}^{2} (4)

Solving for U_{1}:

U_{1} = [NPSHR/K_{3}]^{0.5} (5)

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

E_{s} = U_{1} x S = [NPSHR/K_{3} ]^{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:

E_{s} = [ 1/K_{3}]^{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 U_{1} cuts off two of the legs.

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