Problem 4.9.4:

Water is being pumped to a location that is 35 feet high though a piping network that offers a head loss as h_L (foot pound-force per pound-mass) equal to 0.002 Q² where Q is given in gallons per minute. At the point of operation, pump delivers 200 gallons per minute at a head of 75 foot pound-force per pound-mass. Pump characteristic curve (Q-H) is given as (0, 100), (110, 90), (180, 80), (250, 60), (300, 40), (340, 20). What is the flow rate that can be handled for the flowing cases: (1) one pump, (2) two pumps in series, (3) two pumps in parallel.

Solution:

Required static head is equal to delta Z g over g_c plus h_L. Plugging in the values h is 35 plus 0.002 Q². Writing pump characteristic curves for the given cases:

Q System Single Series Parallel

h H_a H_b H_c

0 35 100 200 100

110 59.2 90 180

180 99.8 80 160

220 131.8 90

250 160 60 120

300 215 40 80

340 266.2 20 40

360 294.2 80

500 535 60

600 755 40

680 959.8 20

Pump characteristic curves can be drawn for different cases, H_a, H_b, and H_c. We can also draw system curve h versus Q.

The intersection of characteristic curves for H_a, H_b, and H_c with system curve h is at 156, 224 and 170 gpm.