---
title: "Design pipes AB and BC, 20,000 population, f = 0.04"
subject: "Water Supply Engineering"
chapter: 7
key: "semester_5/water_supply_engineering:pd-b66"
source: https://www.bctengineer.com/q/semester_5/water_supply_engineering/pd-b66
site: BCT Engineering
---

# Design pipes AB and BC, 20,000 population, f = 0.04

Water Supply Engineering · Chapter 7: Reservoirs and Distribution System

- Asked in: 2066 Bhadra (old course)
- 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-b66
- Whole chapter: https://www.bctengineer.com/md/semester_5/water_supply_engineering/chapter-7

## Question

A part of water distribution system is shown in figure below. The average water requirement is 150 lpcd and water is distributed only from the service reservoir located at A for the population of 20,000 at the point C. Design pipes AB and BC. The minimum pressure to be maintained is 15 m and Darcy's coefficient of friction f is 0.04. Assume peak factor of 3. Calculate the velocity of water in pipes AB and BC.

[Figure: A (RL 200 m) to B (RL 170 m), length 1000 m; B to C (RL 150 m), length 500 m.]

## Short answer

Use Darcy-Weisbach equation with f=0.04. For AB, calculated 299 mm, adopt 300 mm, velocity 1.47 m/s. For BC, calculated 245 mm, adopt 250 mm, velocity 2.12 m/s.

## Answer

#### Given data and flow
- Population at C = 20,000, 150 lpcd, peak factor 3
- $Q = 20000 \times 150 \times 3/86400 = 104.17$ lps $= 0.1042$ m³/s (the full flow passes through both AB and BC)
- RL: A = 200 m (HGL = 200 m), B = 170 m, C = 150 m; $L_{AB} = 1000$ m, $L_{BC} = 500$ m
- Minimum pressure 15 m (at B and C), Darcy friction factor $f = 0.04$

#### Formula
$$
h_f = \frac{8 f L Q^2}{\pi^2 g D^5} \quad\Rightarrow\quad D = \left(\frac{8 f L Q^2}{\pi^2 g\, h_f}\right)^{1/5}
$$

#### Pipe AB
- Available head $= 200 - 170 - 15 = 15$ m
- $D = \left(\dfrac{8 \times 0.04 \times 1000 \times 0.1042^2}{\pi^2 \times 9.81 \times 15}\right)^{1/5} = 299$ mm; adopt **300 mm**
- Actual $h_f = 14.76$ m; HGL at B $= 200 - 14.76 = 185.24$ m; residual head at B $= 15.24$ m (> 15 m, OK)
- Velocity $v = 0.1042/(\pi \times 0.3^2/4) = 1.47$ m/s

#### Pipe BC
- Available head $= 185.24 - 150 - 15 = 20.24$ m
- $D = 245$ mm; adopt **250 mm**
- Actual $h_f = 18.36$ m; HGL at C $= 166.88$ m; residual head at C $= 16.88$ m (> 15 m, OK)
- Velocity $v = 0.1042/(\pi \times 0.25^2/4) = 2.12$ m/s

**Answer: AB = 300 mm with v = 1.47 m/s; BC = 250 mm with v = 2.12 m/s.** Both velocities are below 3 m/s, and the pressure at B and C stays above 15 m.

## Check yourself

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

1. How is the design flow for AB and BC found?
   A. Population x 150 x 3 / 86400, as the full flow passes both pipes
   B. Population x 150 / 86400 only
   C. Half the flow in each pipe
   D. Flow equals the velocity times 1 m
   Answer: A. Q = 20000 x 150 x 3/86400 = 104.17 lps, since all water goes to C through both pipes. (Key point: Design discharge)

2. With Darcy friction factor f, the diameter is found from:
   A. D = (hf / (8 f L Q^2))
   B. h_f = 8 f L Q^2 / (pi^2 g D^5), solved for D
   C. h_f = 10.67 L Q^1.852 / (C^1.852 D^4.87)
   D. h_f = f L v / D
   Answer: B. Darcy-Weisbach h_f = 8fLQ^2/(pi^2 g D^5) is rearranged for D since f is given. (Key point: Formula for diameter)

3. Available head for AB (A = 200 m, B = 170 m, 15 m residual) is:
   A. 30 m
   B. 45 m
   C. 15 m
   D. 10 m
   Answer: C. 200 - 170 - 15 = 15 m. (Key point: Head available for AB)

4. BC has D = 250 mm and Q = 0.1042 m^3/s. Its velocity is about:
   A. 1.47 m/s
   B. 2.12 m/s
   C. 3.5 m/s
   D. 0.5 m/s
   Answer: B. v = Q/A = 0.1042/(pi x 0.25^2/4) = 2.12 m/s. (Key point: Velocity)

## Related in Water Supply Engineering

- [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
- [Design pipes AB and BC, 75 lpcd, tank 6 m high](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-b81) — Water Supply Engineering, chapter 7
- [Service reservoir capacity, 150,000 population](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-c75) — Water Supply Engineering, chapter 7
- [Design pipes RA and AB; 200 lpcd, peak factor 3](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c69) — 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
- [Service reservoir of 30 m diameter, 1,00,000 population](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-bk79) — Water Supply Engineering, chapter 7

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