Design pipes AB and BC, 75 lpcd, tank 6 m high

Data: C = 100, peak (maximum) demand = 3 × average, 75 lpcd, minimum residual head 5.0 m. The tank at A stands 6 m high, so the HGL at A = 2160 + 6 = 2166 m. The population of each section is taken as drawn at its end point (B for AB, C for BC), so pipe AB carries the demand of 850 + 480 = 1330 people and BC carries 480 people.

• $Q_{AB} = 1330 \times 75 \times 3/86400 = 3.464$ lps
• $Q_{BC} = 480 \times 75 \times 3/86400 = 1.250$ 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 $Q = 3.464$ lps, length $L = 400$ m
• HGL at A = 2166.00 m; ground RL at B = 2125 m; residual head required = 5 m
• Available head $H = 2166.00 - 2125 - 5 = 36.00$ m
• Gradient $S = H/L = 36.00/400 = 0.09000$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 53.7$ mm, adopt commercial size 65 mm
• Actual $h_f = 14.143$ m, HGL at B = 2151.86 m, residual head = 26.86 m (≥ 5 m, OK)
• Velocity $v = Q/A = 1.04$ m/s

Pipe BC

• Discharge $Q = 1.250$ lps, length $L = 500$ m
• HGL at B = 2151.86 m; ground RL at C = 2115 m; residual head required = 5 m
• Available head $H = 2151.86 - 2115 - 5 = 31.86$ m
• Gradient $S = H/L = 31.86/500 = 0.06371$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 39.1$ mm, adopt commercial size 40 mm
• Actual $h_f = 28.483$ m, HGL at C = 2123.37 m, residual head = 8.37 m (≥ 5 m, OK)
• Velocity $v = Q/A = 0.99$ m/s

Summary

Velocities are between 0.6 m/s and 3 m/s, so the sizes are acceptable.

Answer: AB = 65 mm and BC = 40 mm; residual heads 26.9 m at B and 8.4 m at C (both more than 5 m); velocities 1.04 m/s and 0.99 m/s.