CIVIL ENGINEERING FORMULAS

342 CHAPTER TWELVE

function of the design. Information on the design is furnished by the pump manu-
facturer in a series of curves for a given pump. Pump efficiency Ep—the ratio of
the useful output power of the pump to the input power to the pump—is given by

(SI units) (12.151)

(U.S. customary units) (12.152)

where Eppump efficiency, dimensionless
Pipower input, kW, kNm/s
specific weight of water, kN/m^3 (lb/ft^3 )
Qcapacity, m^3 /s (ft^3 /s)
Httotal dynamic head, m (ft)
bhpbrake horsepower
550 conversion factor for horsepower to ftlbf/s

Pump efficiencies usually range from 60 to 85 percent.

Characteristic Relationships for Centrifugal Pumps

The relationships described in the following are used to predict the perfor-
mance of centrifugal pumps at rotational speeds other than those for which
pump characteristic curves (pump curves) were developed.

Flow, Head, and Power Coefficients. In centrifugal pumps, similar flow
patterns occur in a series of geometrically similar pumps. By applying the
principles of dimensional analysis and the procedure proposed by Buckingham,
the following three independent dimensionless groups can be derived to describe
the operation of rotodynamic machines including centrifugal pumps:

(12.153)

(12.154)

(12.155)

whereCQflow coefficient
Qcapacity
Nspeed, rev/min
Dimpeller diameter
CHhead coefficient
Hhead
CPpower coefficient
Ppower input

CP

P

N^3 D^5

CH

H

N^2 D^2

CQ

Q

ND^3

Ep

pump output

bhp



QHt

bhp 550

Ep

pump output

Pi



QHt

Pi