Design pipes AB, BC; 160 lpcd, peak factor 3

Per capita demand 160 lpcd, peak factor 3, C = 100, minimum residual head 10 m. HGL at A = 1000 m. The population along each section is taken as supplied at its end node: AB carries the demand of 3600 + 4400 = 8000 people, and BC carries 4400 people.

• $Q_{AB} = 8000 \times 160 \times 3/86400 = 44.44$ lps
• $Q_{BC} = 4400 \times 160 \times 3/86400 = 24.44$ lps

Method

Use the Hazen-Williams equation in SI units:

$$h_f = \frac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$$

with $Q$ in m³/s, $L$ and $D$ in m. For each pipe the available head is (HGL at upstream end − ground RL of the tap − required residual head). The gradient $S = H/L$ gives the calculated diameter, the next larger commercial size is adopted, and the real head loss and residual head are then checked. Commercial sizes (nominal bore): 15, 20, 25, 32, 40, 50, 65, 80, 100, 125, 150, 200 mm and so on. Constant C = 100.

Pipe AB

• Discharge $Q = 44.444$ lps, length $L = 200$ m
• HGL at A = 1000.00 m; ground RL at B = 950 m; residual head required = 10 m
• Available head $H = 1000.00 - 950 - 10 = 40.00$ m
• Gradient $S = H/L = 40.00/200 = 0.20000$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 120.2$ mm, adopt commercial size 150 mm (raised from the head-based size because velocity would exceed 3 m/s)
• Actual $h_f = 13.595$ m, HGL at B = 986.40 m, residual head = 36.40 m (≥ 10 m, OK)
• Velocity $v = Q/A = 2.52$ m/s

Pipe BC

• Discharge $Q = 24.444$ lps, length $L = 500$ m
• HGL at B = 986.40 m; ground RL at C = 900 m; residual head required = 10 m
• Available head $H = 986.40 - 900 - 10 = 76.40$ m
• Gradient $S = H/L = 76.40/500 = 0.15281$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 101.2$ mm, adopt commercial size 125 mm
• Actual $h_f = 27.296$ m, HGL at C = 959.11 m, residual head = 59.11 m (≥ 10 m, OK)
• Velocity $v = Q/A = 1.99$ m/s

Summary

Answer: AB = 150 mm and BC = 125 mm. For AB the head-based size is 125 mm, but its velocity would be 3.6 m/s, which is too high, so 150 mm is adopted (v = 2.5 m/s). Residual heads are above 10 m at B and C.