Case: Operating point for a pump:

If pump characteristic curve is given for a pump, and it is required to obtain an operating point, then the system-head curve need to be constructed as follows:

Where c is a considered to be fairly independent of capacity Q. In a system with gravity head (negative lift) fluid flow will continue until the system friction loss equals the available gravity head. The point of intersection, A, between the H-Q and system curves is the operating point of the pump. When pipes of different sizes are used, the system head curve shifts in such a way that "higher head" can be obtained for a smaller diameter for same capacity Q.

Example 4.21: Two reservoirs are connected with a long pipe which has characteristics such that the head loss through the pipe is expressed as h_fs = 0.002 Q², where h_fs is in ft·lb_f/lb and Q is the flow rate in gpm. The water surface elevation in reservoir B is 35 feet above that in reservoir A. Two identical pumps are available to pump the water from A to B. The characteristic curve of the pump when operating at 1800 rpm is given below:

Ha/ft	100	90	80	60	40	20
Qa/gpm	0	110	180	250	300	340

Find the rate of flow under the following operating conditions: a) single pump; b) two pumps in series; and c) two pumps in parallel, each operating at 1800 rpm.

Solution: Total static head = 35 feet, Frictional head = 0.002 Q². System curve is given as

Draw a system head (h-Q) curve. Intersection of system head-curve and pump head-capacity (H_a-Q_a) curve can be seen to occur at 156 gpm at a head of 83.6 ft.

If another pump is added in series, then head H is to be doubled for given Q. The pump-head capacity (H_b-Q_b) curve will be

Hb/ft	200	180	160	120	80	40
Qb/gpm	0	110	180	250	300	340

This system curve does not change. Now the intersection of the pump-head capacity (H_b-Q_b) curve and the system curve can be found to be at 224 gpm and 135.4 ft.

If a pump is added in parallel, then new Q is twice the original value for a given H.

Hc/ft	100	90	80	60	40	20
Qc/gpm	0	220	360	500	600	680

Now the intersection of the pump-head capacity (H_c-Q_c) curve and the system curve can be found to be at 170 gpm and 92.8 ft. The intersection of H_a, H_b, and H_c curves with the system curve h occurs at 156 gpm, 224 gpm, and 170 gpm, respectively.