Page 416 - 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 E —the ratio of
p
the useful output power of the pump to the input power to the pump—is given by
pump output QH t
E p (SI units) (12.151)
P i P i
pump output QH t
E p (U.S. customary units) (12.152)
bhp bhp 550
where E pump efficiency, dimensionless
p
P power input, kW, kN m/s
i
3
3
specific weight of water, kN/m (lb/ft )
3
3
Q capacity, m /s (ft /s)
H total dynamic head, m (ft)
t
bhp brake horsepower
550 conversion factor for horsepower to ft lb /s
f
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:
Q
C Q (12.153)
ND 3
H
C H (12.154)
2
N D 2
P
C P (12.155)
3
N D 5
where C flow coefficient
Q
Q capacity
N speed, rev/min
D impeller diameter
C head coefficient
H
H head
C power coefficient
P
P power input