---
title: "Circular sewer just full, 1.6 m³/s"
subject: "Sanitary Engineering"
chapter: 3
key: "semester_6/sanitary_engineering:sewer-just-full-1p6-slope-1-150"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-just-full-1p6-slope-1-150
site: BCT Engineering
---

# Circular sewer just full, 1.6 m³/s

Sanitary Engineering · Chapter 3: Design and Construction of Sewers

- Asked in: 2078 Chaitra, 8 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-just-full-1p6-slope-1-150
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3

## Question

Calculate the diameter of a circular sewer laying at a slope of 1:150 when it is running just full with a discharge of 1.6 m³/sec and Manning's coefficient 0.013. Also, determine the discharge capacity if it is permitted to flow half full with the same gradients.

## Short answer

Manning's equation for full flow yields D = 0.927 m (adopt 1.05 m). At half full, discharge is exactly half of full capacity, i.e., 0.80 m³/s, with the same velocity 2.37 m/s.

## Answer

#### Part 1: Diameter when running just full
For a circular pipe flowing full, $Q=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$, with $S=1/150=0.006667$ and $n=0.013$:

$$
D=\left(\frac{Q\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{1.6\times0.013}{0.3117\times0.08165}\right)^{3/8}=0.927\ \text{m}
$$

Full velocity: $v_f=\dfrac{Q}{A}=\dfrac{1.6}{\frac{\pi}{4}(0.927)^2}=2.37$ m/s (check: $\frac{0.3969}{n}D^{2/3}S^{1/2}=2.37$ m/s).

Adopt a standard diameter of 1.05 m (the calculated size 0.927 m is the minimum required).

#### Part 2: Discharge when half full
At $d/D=0.5$: $A=A_f/2$ and $R=R_f$, so $v=v_f$ and with $n$ constant,

$$
Q_{half}=\frac{Q_f}{2}=\frac{1.6}{2}=0.80\ \text{m}^3/\text{s}
$$

(for the calculated diameter; for the adopted $D=1.05$ m the half-full capacity is $1.115$ m³/s).

**Answer: D = 0.927 m (adopt 1.05 m); half-full discharge = 0.80 m³/s with the same velocity 2.37 m/s.**

## Check yourself

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

1. Which formula gives the diameter of a sewer running just full?
   A. D = (Q n / (0.3117 S^(1/2)))^(3/8)
   B. D = (Q n / (0.3117 S^(1/2)))^(8/3)
   C. D = (Q / (v n))^(1/2)
   D. D = Q S / n
   Answer: A. From Manning's full-pipe equation Q = (0.3117/n) D^(8/3) S^(1/2); D = 0.927 m here. (Key point: Diameter running full)

2. What is the discharge of the same sewer running half full at the same gradient?
   A. 1.6 m3/s, the same
   B. 0.40 m3/s
   C. 0.80 m3/s, half of the full discharge
   D. 1.13 m3/s
   Answer: C. At half depth v = v_f and area is half, so Q = Q_f/2 = 0.8 m3/s. (Key point: Half-full discharge)

3. What is the velocity at half depth compared with the full velocity?
   A. Half of the full velocity
   B. Equal to the full velocity, 2.37 m/s
   C. Twice the full velocity
   D. 1.12 times the full velocity
   Answer: B. R = D/4 at both full and half-full flow, so Manning velocity is unchanged. (Key point: Velocity at half depth)

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