If two pumps with head-discharge characteristics plotted in Figure 4.10 (dashed lines) are to be used, (a) determine the pumping system discharges when each pump is operated separately and, when both pumps are operated in parallel (b), determine at what head will both pumps operated in series deliver a discharge of 0.2 m /s.

Solution: (a) The system head-discharge or head-capacity curve is plotted as shown in the figure. The pump head-discharge curves supplied by the manufacturer (dashed lines) are modified by the head losses as given above. The resulting effective head-discharge curves are drawn in solid lines designated as mP1 and mP2 for pumps 1 and 2, respectively. The intersection of the effective head-discharge curve and the system curve, when only pump no. 1 is operating, is 0.2 m /s. This is the pumping system discharge. Ans

When only pump no. 2 is operating, the system discharge is 0.31 m /s. Ans When both are operated in parallel, the effective characteristic curve for pump no. 1 is shifted horizontally to the right until the top end of the curve coincides with a portion of the effective curve of pump no. 2, as shown. This has the effect of adding the discharges for parallel operation. As indicated, when both are operated in parallel, the system discharge is 0.404 m /s. Ans

(b) For the operation in series, the TDH for pump no. 1 for a system discharge of 0.2 m2/s is 13 m. That of pump no. 2 is 32 m. Therefore, the system TDH is 32 + 13 = 45 m. Ans glossary

Axial-flow pumps—Pumps that transmit the fluid pumped in the axial direction. Best operating efficiency—Value of the efficiency that corresponds to the best operating performance of the pump. Brake or shaft power—The power of the motor or prime mover driving the pump.

Brake efficiency—Ratio of the power given to the fluid to the brake input power

(brake power) to the pump. Cavitation—A state of flow where the pressure in the liquid becomes equal to its vapor pressure.

Centrifugal pump—A pump that conveys fluid through the momentum created by a rotating impeller. Discharge—In a pumping system, the arrangement of elements after the pumping station.

Discharge velocity head—The velocity head at the discharge of a pumping system.

Displacement pumps—Pumps that literally pushes the fluid in order to move it.

Dynamically similar pumps—Pumps with head coefficients that are equal.

Fittings losses—Head losses in valves and fittings.

Flow coefficient Cq—The group Q/(oD ).

Friction head loss—A head loss due to loss of internal energy.

Gear pump—A pump that basically operate like a lobe pump, except that instead of lobes, gear teeth are used to move the fluid.

Geometrically similar pumps—Pumps with corresponding parts that are proportional.

Head coefficient CH—The group Hg/(o}DD2).

Homologous pumps—Pumps that are similar. Similarities are established dynamically, kinematically, or geometrically.

Inlet dynamic head—The sum of the inlet velocity head and inlet manometric head of a pump.

Inlet manometric head—The manometric level at the inlet to a pump.

Kinematically similar pumps—Pumps whose flow coefficients are equal.

Lobe pump—A positive-displacement pump whose impellers are shaped like lobes.

Manifold pipe—A pipe with two or more pipes connected to it.

Manometric level—The height of liquid corresponding to the gage pressure.

Mixed-flow pump—Pump with an impeller that is designed to provide a combination of forward and radial flow.

Net positive suction head (NSPH)—The amount of energy possessed by a fluid at the inlet to a pump.

Non-pivot parameter—The counterpart of pivot parameter.

Outlet dynamic head—The sum of the outlet velocity head and outlet mano-metric head of a pump.

Outlet manometric head—The manometric level at the outlet of a pump.

Parallel connection—Mode of connection of more than one pump where the discharges of all the pumps are combined into one.

Positive-displacement pump—A pump that conveys fluid by directly moving it using a suitable mechanism such as a piston, plunger, or screw.

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