Design pipelines AB, BC and CD, C = 120

Hazen-Williams constant C = 120; the residual pressure at B, C and D must be at least 12 m. HGL at A = RL of A = 500 m.

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 = 120.

Pipe AB

• Discharge $Q = 0.250$ lps, length $L = 700$ m
• HGL at A = 500.00 m; ground RL at B = 480 m; residual head required = 12 m
• Available head $H = 500.00 - 480 - 12 = 8.00$ m
• Gradient $S = H/L = 8.00/700 = 0.01143$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 28.1$ mm, adopt commercial size 32 mm
• Actual $h_f = 4.281$ m, HGL at B = 495.72 m, residual head = 15.72 m (≥ 12 m, OK)
• Velocity $v = Q/A = 0.31$ m/s

Pipe BC

• Discharge $Q = 0.150$ lps, length $L = 500$ m
• HGL at B = 495.72 m; ground RL at C = 465 m; residual head required = 12 m
• Available head $H = 495.72 - 465 - 12 = 18.72$ m
• Gradient $S = H/L = 18.72/500 = 0.03744$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 18.2$ mm, adopt commercial size 20 mm
• Actual $h_f = 11.711$ m, HGL at C = 484.01 m, residual head = 19.01 m (≥ 12 m, OK)
• Velocity $v = Q/A = 0.48$ m/s

Pipe CD

• Discharge $Q = 0.100$ lps, length $L = 600$ m
• HGL at C = 484.01 m; ground RL at D = 440 m; residual head required = 12 m
• Available head $H = 484.01 - 440 - 12 = 32.01$ m
• Gradient $S = H/L = 32.01/600 = 0.05335$
• From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 14.5$ mm, adopt commercial size 15 mm
• Actual $h_f = 26.922$ m, HGL at D = 457.09 m, residual head = 17.09 m (≥ 12 m, OK)
• Velocity $v = Q/A = 0.57$ m/s

Summary

The pipe sizes are small because the flows are only a few tenths of a litre per second, and the velocities (0.3–0.6 m/s) are low; they are acceptable for a rural system with the limited head available. Maximum static head is at D: 500 − 440 = 60 m, so a pipe class for 60 m (about 0.6 MPa) is needed.

Answer: AB = 32 mm, BC = 20 mm, CD = 15 mm.