Design pipes RA and AB; 200 lpcd, peak factor 3

Per capita demand 200 lpcd, peak factor 3, C = 100, residual head ≥ 15 m. HGL at R = 890 m. The population along each section is treated as drawn at its end node (A for RA, B for AB): pipe RA carries 3600 + 4400 = 8000 people and AB carries 4400 people.

• $Q_{RA} = 8000 \times 200 \times 3/86400 = 55.56$ lps
• $Q_{AB} = 4400 \times 200 \times 3/86400 = 30.56$ 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 RA

• Discharge $Q = 55.556$ lps, length $L = 200$ m
• HGL at R = 890.00 m; ground RL at A = 840 m; residual head required = 15 m
• Available head $H = 890.00 - 840 - 15 = 35.00$ m
• Gradient $S = H/L = 35.00/200 = 0.17500$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 134.5$ mm, adopt commercial size 200 mm (raised from the head-based size because velocity would exceed 3 m/s)
• Actual $h_f = 5.063$ m, HGL at A = 884.94 m, residual head = 44.94 m (≥ 15 m, OK)
• Velocity $v = Q/A = 1.77$ m/s

Pipe AB

• Discharge $Q = 30.556$ lps, length $L = 500$ m
• HGL at A = 884.94 m; ground RL at B = 790 m; residual head required = 15 m
• Available head $H = 884.94 - 790 - 15 = 79.94$ m
• Gradient $S = H/L = 79.94/500 = 0.15987$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 109.1$ mm, adopt commercial size 125 mm
• Actual $h_f = 41.264$ m, HGL at B = 843.67 m, residual head = 53.67 m (≥ 15 m, OK)
• Velocity $v = Q/A = 2.49$ m/s

Summary

The head-based diameter of RA is 134.5 mm, but 150 mm would give a velocity of 3.14 m/s, which is above the usual limit of 3 m/s; 200 mm is therefore adopted (v = 1.77 m/s). All velocities are between 0.6 and 3 m/s and all residual heads are above 15 m.

Answer: RA = 200 mm, AB = 125 mm.