CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 343

The operating points at which similar flow patterns occur are called corre-
sponding points;the Eqs. (12.153) to (12.155) apply only to corresponding
points. However, every point on a pump head-capacity curve corresponds to a
point on the head-capacity curve of a geometrically similar pump operating at
the same speed or a different speed.

Affinity Laws. For the same pump operating at a different speed, the diameter
does not change and the following relationships can be derived from Eqs. (12.153)
through (12.155):

(12.156)

(12.157)

(12.158)

These relationships, collectively known as the affinity laws,are used to
determine the effect of changes in speed on the capacity, head, and power of a
pump.

Specific Speed. For a geometrically similar series of pumps operating under
similar conditions, the specific speed is

(12.159)

whereNsspecific speed
Nspeed, rev/min
Qcapacity, m^3 /s (gal/min)
Hhead, m (ft)

To obtain the specific speed based on U.S. customary units of head and
capacity, multiply the specific speed based on metric units of head and capacity
by 52.
For any pump operating at any given speed, QandHare taken at the point
of maximum efficiency. When using Eq. (12.159) for pumps having double-
suction impellers, one-half of the discharge is used, unless otherwise noted. For
multistage pumps, the head is the head per stage.

Cavitation

When determining if cavitation will be a problem, two different net positive
suction heads (NPSH or hsv) are used. The NPSH available (NPSHA) is the
NPSH available in the system at the eye of the impeller. The NPSH required
(NPSHR) is the NPSH required at the pump to prevent cavitation in the pump.
The NPSHAis the total absolute suction head, as given by Eq. (12.149) above

Ns

C^1 Q^2

C^1 H^2



(QND^3 )^1 ^2

(HN^2 D^2 )^3 ^4



NQ^1 ^2

H^3 ^4

P 1

P 2



N^31

N^32

H 1

H 2



N^21

N^22

Q 1

Q 2



N 1

N 2