Page 415 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 341

where H total dynamic head, m (ft)
t
H (H ) discharge (suction) head measured at discharge (suction) nozzle
d S
of pump referenced to the centerline of the pump impeller, m (ft)
V (V ) velocity in discharge (suction) nozzle, m/s (ft/s)
d s
2
2
g acceleration due to gravity, 9.81 m/s (32.2 ft/s )
h (h ) static discharge (suction) head, m (ft)
d s
h (h ) frictional head loss in discharge (suction) piping, m (ft)
fd fg
h (h ) minor fitting and valve losses in discharge (suction) piping
md ms
system, m (ft). Entrance loss is included in computing the
minor losses in the suction piping.
The reference datum for writing Eq. (12.146) is taken as the elevation of the
centerline of the pump impeller. In accordance with the standards of the
Hydraulic Institute, distances (heads) above datum are considered positive; dis-
tances below datum are considered negative.
In terms of the static head, Eq. (12.146) can be written as
2
V d
H t H stat h fs
h ms h fd
h md (12.149)
2g
where H total dynamic head, m (ft)
t
H stat total static head, m (ft)
h – h s
d
2
In Eq. (12.149), the energy in the velocity head V d 2g is usually considered to
be lost at the outlet of the piping system. In practice, this loss of energy is taken
as being equivalent to the exit loss and is included as a minor loss.
The energy (Bernoulli’s) equation can also be applied to determine the total
dynamic head on the pump. The energy equation written between the suction
and discharge nozzle of the pump is
2 2
H t P d V d z d P s V s z s (12.150)
2g 2g
where H total dynamic head, m (ft)
t
2
2
P (P ) discharge (suction) gage pressure, kN/m (lb /ft )
f
s
d
3
3
specific weight of water, N/m (lb /ft )
f
V (V ) velocity in discharge (suction) nozzle, m/s (ft/s)
d
s
2
2
g acceleration due to gravity, 9.81 m/s (32.2 ft/s )
z (z ) elevation of zero of discharge (suction) gage above datum, m (ft)
s
d
Head losses within the pump are incorporated in the total dynamic head term in
Eq. (12.150).
Pump Efficiency and Power Input
Pump performance is measured in terms of the capacity that a pump can dis-
charge against a given head and at a given efficiency. The pump capacity is a