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274 Chapter 8 Pumping, Storage, and Dual Water Systems
parallel. Characteristic curves for other multiple units are developed in the same way from
the known curves of individual units.
Where most of the operating head is static lift—when the water is pumped through
relatively short lengths of suction and discharge piping, for example—there is little
change in the system head at different rates of flow. In these circumstances, the head
curve is nearly horizontal, and the discharge of parallel pumps is substantially additive.
This is common in wastewater pumping stations in which the flow is lifted from a lower
to an immediately adjacent higher level. Examples are pumping stations along intercep-
tors or at outfalls.
By contrast, friction may control the head on pumps discharging through long force
mains, and it may not be feasible to subdivide flows between pumping units with reason-
able efficiency. Multispeed motors or different combinations of pumps and motors may
then be required.
Because flows from a number of pumps may have to be fed through a different piping
system than flows from any single unit, it may be necessary to develop “modified” charac-
teristic curves that account for losses in different combinations of piping.
Centrifugal pumps are normally operated with discharge velocities of 5 to 15 ft/s (1.5
to 4.6 m/s). The resulting average outlet diameter of the pump, called the pump size, can be
determined by the following two equations:
D podin = 0.21Q (U.S. Customary Units) (8.17)
where D podin is the pump outlet diameter, in; and Q is the capacity of the pump, gpm;
and
D podcm = 63.951Q (SI Units) (8.17a)
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where Q is the capacity of the pump, m /s; and D podcm is the pump outlet diameter, cm. For
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instance, when the capacity of the pump is 200 gpm (0.01262 m /s 12.62 L/s), the out-
let diameter of the pump should be 2.8284 in. (7.1841 cm). An engineer may select 3 in.
(75 mm) as the outlet diameter.

EXAMPLE 8.4 SELECTION OF PUMPS COMBINATION TO SATISFY WATER DEMAND
A mill supply drawing relatively large quantities of water from a river is to deliver them at
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a fairly low head. The minimum demand is 10 MGD (0.438 m /s), the normal 35 MGD
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(1.53 m /s), and the maximum 50 MGD (2.19 m /s). The river fluctuates in level by 5 ft (1.52 m),
and the working range of a balancing tank is 15 ft (4.57 m). The vertical distance between the
bottom of the tank and the surface of the river at its high stage is 60 ft (18.3 m). The friction head
in the pumping station and a 54-in. (76.2-cm) force main rises from a minimum of 1 ft (0.30 m)
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at the 10-MGD (0.438 m /s) rate to a maximum of nearly 20 ft (6.1 m) at the 50-MGD
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(2.19 m /s) rate. Make a study of suitable pumping units, knowing that 1 MGD 3.785 MLD
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0.0438 m /s 43.8 L/s.
Solution:
The solution to this problem is shown in Fig. 8.5. Three pumps are provided: No. 1 with a capacity
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of 15 MGD (0.657 m /s 657 L/s) at 66-ft (20.117-m) head; No. 2 with 25 MGD (1.059 m /s
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1,059 L/s) at 78-ft (23.774-m) head; and No. 3 with 37 MGD (1.62 m /s 1,620 L/s) at 84-ft (25.6-m)
head. Each pump has an efficiency of 89% at the design point. The efficiencies at the top and bot-
tom of the working range are listed in Table 8.1.