---
title: "Design pipelines AB and BC, C = 100, 10 m head"
subject: "Water Supply Engineering"
chapter: 7
key: "semester_5/water_supply_engineering:pd-c70"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pd-c70
site: BCT Engineering
---

# Design pipelines AB and BC, C = 100, 10 m head

Water Supply Engineering · Chapter 7: Reservoirs and Distribution System

- Asked in: 2070 Chaitra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pd-c70
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-7

## Question

A layout of water distribution is shown in the figure below. Design pipelines AB and BC considering Hazen-William's Coefficient = 100. Minimum pressure required at B and C is 10 m of water.

[Figure: River source near A, RL = 950 m; A to B: discharge 1.3 lps, L = 2750 m, RL of B = 920 m; B to C: L = 1700 m, RL of C = 894 m.]

## Short answer

Use Hazen-Williams equation with C=100. Pipe AB (1.3 lps, 2750 m) adopts 65 mm and pipe BC (0.65 lps, 1700 m) adopts 40 mm. Residual heads are 14.16 m at B and 11.32 m at C.

## Answer

C = 100; minimum residual pressure at B and C = 10 m. HGL at A = 950 m. The discharge in BC is not given in the figure; it is assumed that half of the 1.3 lps is used at B, so BC carries 0.65 lps (if the actual discharge is known, substitute it in the same steps).

#### 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 $Q = 1.300$ lps, length $L = 2750$ m
- HGL at A = 950.00 m; ground RL at B = 920 m; residual head required = 10 m
- Available head $H = 950.00 - 920 - 10 = 20.00$ m
- Gradient $S = H/L = 20.00/2750 = 0.00727$
- From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 62.0$ mm, adopt commercial size **65 mm**
- Actual $h_f = 15.836$ m, HGL at B = 934.16 m, residual head = 14.16 m (≥ 10 m, OK)
- Velocity $v = Q/A = 0.39$ m/s

#### Pipe BC
- Discharge $Q = 0.650$ lps, length $L = 1700$ m
- HGL at B = 934.16 m; ground RL at C = 894 m; residual head required = 10 m
- Available head $H = 934.16 - 894 - 10 = 30.16$ m
- Gradient $S = H/L = 30.16/1700 = 0.01774$
- From $h_f = \dfrac{10.67\,L\,Q^{1.852}}{C^{1.852}D^{4.87}}$: $D_{calc} = 39.6$ mm, adopt commercial size **40 mm**
- Actual $h_f = 28.847$ m, HGL at C = 905.32 m, residual head = 11.32 m (≥ 10 m, OK)
- Velocity $v = Q/A = 0.52$ m/s

#### Summary
| Pipe | Q (lps) | L (m) | Calc. D (mm) | Adopted D (mm) | h_f (m) | Residual (m) | v (m/s) |
|---|---|---|---|---|---|---|---|
| AB | 1.3 | 2750 | 62.0 | 65 | 15.84 | 14.16 | 0.39 |
| BC | 0.65 | 1700 | 39.6 | 40 | 28.85 | 11.32 | 0.52 |

**Answer: AB = 65 mm and BC = 40 mm (GI), with residual heads of 14.2 m at B and 11.3 m at C.**

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. HGL at A 950, B at 920, residual 10 m. Available head?
   A. 30 m
   B. 20 m
   C. 40 m
   D. 10 m
   Answer: B. 950 - 920 - 10 = 20 m. (Key point: Available head AB)

2. What commercial sizes result?
   A. AB 65 mm, BC 40 mm
   B. AB 40 mm, BC 65 mm
   C. AB 62 mm, BC 39.6 mm
   D. Both 50 mm
   Answer: A. Calculated 62.0 and 39.6 mm round up to 65 and 40 mm. (Key point: Final sizes)

## Related in Water Supply Engineering

- [Design pipelines AB, BC and CD, C = 120](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c74) — Water Supply Engineering, chapter 7
- [Design pipes AB and BC, source RL 1050 m](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c76) — Water Supply Engineering, chapter 7
- [Design pipes AB and BC, source RL 180 m](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-as67) — Water Supply Engineering, chapter 7
- [Design pipelines AB, BC, AD; 1 kg/cm2 at tap](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c68) — Water Supply Engineering, chapter 7
- [Design pipes AB and BC, A RL 210 m, 44 and 18 lps](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c73) — Water Supply Engineering, chapter 7
- [Design pipes AB, BC; 160 lpcd, peak factor 3](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c71) — Water Supply Engineering, chapter 7

## Related in other subjects

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- [Settling basin with Hazen coefficient and sediment depth](https://www.bctengineer.com/question.md?key=semester_7%2Fhydropower_engineering%3Asettling-basin-hazen-sediment-depth-5000ppm) — Hydropower Engineering, chapter 5
- [Water pipe thickness from pressure head](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Awater-pipe-thickness-pressure-head) — Strength of Materials, chapter 5