From dynamic similarity criteria, the corresponding discharge and
head that a pump can develop with varying speed are written as
Q 2 Q 1 (N 2 /N 1 ) (13.5)
and
H 2 H 1 (N 2 /N 1 )^2. (13.6)
Where the demand for pumping varies (e.g. variation in the inflow
rate during the day at a sewage pumping station) several pumps are oper-
ated in a ‘parallel’ arrangement with any number of pumps brought into
operation according to the level in the suction well (sump). For pumping
against large heads (deep borewell pumping) pumps are operated in
‘series’, i.e. water from the first pump (impeller) is delivered to the inlet of
the second pump, and so on. A pump with impellers in series is also called
a multistage or booster pump. All pumps in the series system must operate
simultaneously.
13.2.5 Pump setting (suction lift)
Referring to Fig. 13.2 application of Bernoulli’s equation between the
sump water level and the pump (impeller) inlet gives
ps/ gpa/ g (hshfsV^2 s/2g). (13.7)
Equation (13.7) indicates that the pressure at the pump inlet, ps, is
below atmospheric pressure, pa, and if this negative pressure exceeds the
vapour pressure limits cavitation sets in. To avoid cavitation (otherwise
the efficiency drops and the impeller becomes damaged) the suction head,
hs, is limited so that the pressure at the inlet is equal to the allowable
vapour pressure pv. Other measures such as minimizing head losses (by
choosing large diameters and shorter lengths of suction pipes without
regulating valves) are also taken.
The maximum suction head (pump setting) can thus be given as
hs(pa pv) g (hfsV^2 s/2g). (13.8)
From equation (13.7) the net positive suction head (NPSH) can be
written as
(ps pv)/ gNPSH(pa pv)/ g (hshfsV^2 s/2g) (13.9)
552 PUMPING STATIONS
