---
title: "Combined sewer, half full, 1.5 m³/s"
subject: "Sanitary Engineering"
chapter: 3
key: "semester_6/sanitary_engineering:combined-sewer-1p5-half-full"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/combined-sewer-1p5-half-full
site: BCT Engineering
---

# Combined sewer, half full, 1.5 m³/s

Sanitary Engineering · Chapter 3: Design and Construction of Sewers

- Asked in: 2079 Chaitra, 8 marks; 2075 Baisakh, 8 marks (asked 2 times)
- Video: [Design of sewers || Wastewater Engineering || Circular Sewer || GATE](https://www.youtube.com/watch?v=bD3bD0YJlHE) — Civil learning online
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/combined-sewer-1p5-half-full
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3

## Question

Determine the size of combined circular sewer for a discharge of 1.5 m³/s running half full. Assume a gradient of 1 in 2000 and Manning's rugosity coefficient N = 0.013 (constant for all flows). In the dry season if the flow drops to 0.5 m³/sec, does the flow maintain desired self-cleaning velocity of 0.60 m/sec?

## Short answer

At half full, full discharge is 3.0 m3/s; using Manning's formula gives D=1.907 m, adopt 2.10 m. Dry-season flow ratio gives velocity about 0.77 m/s, so self-cleaning velocity of 0.60 m/s is maintained.

## Answer

#### Part 1: Size of the sewer
At half depth ($d/D=0.5$) the area and hydraulic radius are half and equal to the full values, respectively: $A=A_f/2$, $R=R_f$, so $v=v_f$ and, with $n$ constant, $Q=Q_f/2$.

$$
Q_f=2\times1.5=3.0\ \text{m}^3/\text{s}
$$

Full-pipe Manning's formula: $Q_f=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$ with $S=\dfrac{1}{2000}=0.0005$, $n=0.013$.

$$
D=\left(\frac{Q_f\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{3.0\times0.013}{0.3117\times0.02236}\right)^{3/8}=1.907\ \text{m}
$$

Adopt a standard size $D=2.10$ m. Check: $v_f=\dfrac{0.3969}{n}D^{2/3}S^{1/2}=1.120$ m/s (this is also the velocity at half depth), $Q_f=3.877$ m³/s, so half-full capacity $=1.939$ m³/s, greater than 1.5 m³/s. Velocity at design flow is above 0.6 m/s.

#### Part 2: Dry-season flow of 0.5 m³/s
Using the adopted $D=2.10$ m, $Q_f=3.877$ m³/s and $v_f=1.120$ m/s:

$$
\frac{Q}{Q_f}=\frac{0.5}{3.877}=0.1290
$$

For circular sections with constant $n$, this ratio corresponds to $d/D=0.243$ (solving $Q/Q_f=\frac{A}{A_f}\left(\frac{R}{R_f}\right)^{2/3}$). Then $\dfrac{v}{v_f}=0.689$ and

$$
v=0.689\times1.120=0.77\ \text{m/s}
$$

Since 0.77 m/s is greater than 0.60 m/s, the flow does maintain the self-cleansing velocity in the dry season.

**Answer:** $D\approx2.10$ m (computed 1.907 m). In the dry season the velocity is about 0.77 m/s, so the self-cleansing velocity is maintained.

## Check yourself

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

1. For a circular sewer running half full with constant n, how do v and Q compare with the full-pipe values?
   A. v = v_f and Q = Q_f/2
   B. v = v_f/2 and Q = Q_f/2
   C. v = v_f and Q = Q_f
   D. v = 2 v_f and Q = Q_f
   Answer: A. At d/D = 0.5 the hydraulic radius equals the full value so velocity is the same, while the area is half, so Q is half. (Key point: Half-full relations)

2. The sewer must carry 1.5 m3/s running half full. What full-pipe discharge is used in Manning's formula to find D?
   A. 1.5 m3/s
   B. 0.75 m3/s
   C. 3.0 m3/s
   D. 4.5 m3/s
   Answer: C. Q = Q_f/2 at half depth, so Q_f = 2 x 1.5 = 3.0 m3/s. (Key point: Full-pipe design discharge)

3. The computed diameter is 1.907 m. What is done next?
   A. Adopt exactly 1.907 m
   B. Adopt the next standard size (2.10 m) and re-check capacity and velocity
   C. Adopt 1.5 m to save cost
   D. Adopt 2.10 m without any check
   Answer: B. Computed D is a minimum; a standard size above it is adopted and checked (half-full capacity 1.939 m3/s > 1.5). (Key point: Adopting standard size)

4. In the dry season Q = 0.5 m3/s in the 2.10 m sewer. How is the velocity found?
   A. Use v = Q_f / A_f directly because the pipe is full
   B. Assume the velocity stays at 1.12 m/s since n is constant
   C. Divide 0.5 by the half-full area
   D. Find Q/Q_f = 0.129, get d/D and v/v_f from the proportionate-flow relations, then v = (v/v_f) x v_f
   Answer: D. Velocity changes with depth; v/v_f = 0.689 at d/D = 0.243 gives v = 0.77 m/s > 0.6 m/s, so self-cleansing is maintained. (Key point: Dry-season self-cleansing check)

## Related in Sanitary Engineering

- [Circular sewer just full, 1.6 m³/s](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-just-full-1p6-slope-1-150) — Sanitary Engineering, chapter 3
- [Combined circular sewer, 35 ha](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-35ha) — Sanitary Engineering, chapter 3
- [Circular combined sewer, 60 ha](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-60ha) — Sanitary Engineering, chapter 3
- [Design discharge of rural combined sewer](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Adesign-discharge-combined-rural) — Sanitary Engineering, chapter 2
- [Sewer diameter and velocity, just full](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-just-full-1-slope-400) — Sanitary Engineering, chapter 3
- [Wet weather discharge, combined sewer](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Awet-weather-discharge-small-town) — Sanitary Engineering, chapter 2

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