The velocity v ft/s in a pipe = g/?m/2.448t/^2. For this pipe, v = 2000/[(2.448)(7.98)^2 )] =
12.82 ft/s (3.91 m/s). Then he = 0.74(12.82)^2 /[2(23.2)] = 1.89 ft (0.58 m), and hex =
(12.82)^2 /[(2)(32.2)] = 2.56 ft (0.78 m). Hence, the total length of the piping system in Fig.
4a is 130 + 56 + 4.5 + 53 + 1.89 + 2.56 = 247.95 ft (75.6 m), say 248 ft (75.6 m).
Use a suitable head-loss equation, or Table 4, to compute the head loss for the pipe
and fittings. Enter Table 4 at an 8-in (203.2-mm) pipe size, and project horizontally across
to 2000 gal/min (126.2 L/s) and read the head loss as 5.86 ft of water per 100 ft
(1.8m/30.5m)ofpipe.
The total length of pipe and fittings computed above is 248 ft (75.6 m). Then total fric-
tion-head loss with a 2000 gal/min (126.2-L/s) flow is Hfft = (5.86)(248/100) = 14.53 ft
(4.5m).
- Compute the total head on the pump
The total head on the pump Ht = Hts + Hf. For the pump in Fig. 4a, //,= 110+ 14.53 =
124.53 ft (37.95 m), say 125 ft (38.1 m). The total head on the pump in Fig. 4b and c
would be the same. Some engineers term the total head on a pump the total dynamic head
to distinguish between static head (no-flow vertical head) and operating head (rated flow
through the pump).
The total head on the pumps in Fig. 4d, C 9 and/is computed in the same way as de-
scribed above, except that the total static head is less because the pump has a static suc-
tion head. That is, the elevation of the liquid on the suction side reduces the total distance
through which the pump must discharge liquid; thus the total static head is less. The static
suction head is subtracted from the static discharge head to determine the total static head
on the pump. - Compute the horsepower required to drive the pump
The brake hp input to a pump bhpt = (gpm)(Ht)(s)/3960e, where s = specific gravity of the
liquid handled; e = hydraulic efficiency of the pump, expressed as a decimal. The usual
hydraulic efficiency of a centrifugal pump is 60 to 80 percent; reciprocating pumps, 55 to
90 percent; rotary pumps, 50 to 90 percent. For each class of pump, the hydraulic effi-
ciency decreases as the liquid viscosity increases.
Assume that the hydraulic efficiency of the pump in this system is 70 percent and the
TABLE 4. Pipe Friction Loss for Water (wrought-iron or steel schedule 40 pipe in
good condition)
Friction loss per
100 ft (30.5m)
Diameter Flow Velocity Velocity head of pipe
in mm gal/min L/s ft/s m/s ft water m water ft water m water
6 152.4 1000 63.1 11.1 3.4 1.92 0.59 6.17 1.88
6 152. 4 200 0 126. 2 22. 2 6. 8 7.6 7 2. 3 23. 8 7.2 5
6 152. 4 400 0 252. 4 44. 4 13. 5 30. 7 9. 4 93. 1 28. 4
8 203. 2 100 0 63. 1 6.4 1 1. 9 0.63 9 0.19 5 1.5 6 0.47 5
8 203. 2 200 0 126. 2 12. 8 3. 9 2.5 6 0.7 8 5.8 6 1.78 6
8 203. 2 400 0 252. 4 25. 7 7. 8 10. 2 3. 1 22. 6 6.88 8
10 254. 0 100 0 63. 1 3.9 3 1. 2 0.24 0 0.0 7 0.49 7 0.15 1
10 254. 0 300 0 189. 3 11. 8 3. 6 2.1 6 0.65 8 4.0 0 1.21 9
10 254. 0 500 0 315. 5 19. 6 5. 9 5.9 9 1.8 2 10. 8 3.29 2