---
title: "Sewer diameter and velocity, just full"
subject: "Sanitary Engineering"
chapter: 3
key: "semester_6/sanitary_engineering:sewer-just-full-1-slope-400"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-just-full-1-slope-400
site: BCT Engineering
---

# Sewer diameter and velocity, just full

Sanitary Engineering · Chapter 3: Design and Construction of Sewers

- Asked in: 2068 Bhadra (old course), 10 marks
- Video: [design of sewer, Quantity of sewage in combined sewer Problem, sewer size and velocity calculation](https://www.youtube.com/watch?v=oCX5F2VnK7Q) — Civil Engineering Exam
- 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-1-slope-400
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3

## Question

Calculate the diameter and velocity of a circular sewer at a slope of 1 in 400 when it is running just full at a discharge of 1 m³/sec. The value of n in Manning's formula is 0.012. Will the self cleansing velocity be maintained in the sewer when flow drops to 0.6 m³/s?

## Short answer

Using Manning's formula with n=0.012, S=1/400, Q=1 m³/s gives diameter 0.907 m and full-flow velocity 1.55 m/s. At 0.6 m³/s, d/D=0.558 and v=1.045×1.55=1.62 m/s, which exceeds the self-cleansing velocity of 0.6 m/s; the condition is maintained.

## Answer

#### Part 1: Diameter and velocity (just full)
$S=1/400=0.0025$, $n=0.012$, $Q=1$ m³/s. For a full circular pipe:

$$
D=\left(\frac{Q\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{1\times0.012}{0.3117\times0.05}\right)^{3/8}=0.907\ \text{m}
$$

$$
v=\frac{Q}{\frac{\pi}{4}D^2}=\frac{1}{\frac{\pi}{4}(0.907)^2}=1.55\ \text{m/s}
$$

(In practice, a standard size such as 975 mm or 1.05 m would be adopted.)

#### Part 2: Check at 0.6 m³/s
For the sewer that runs just full at 1 m³/s ($D=0.907$ m, $Q_f=1$ m³/s, $v_f=1.55$ m/s):

$$
\frac{Q}{Q_f}=\frac{0.6}{1.0}=0.60
$$

From the proportionate-flow relations of a circular section (constant $n$), this gives $d/D=0.558$ and $v/v_f=1.045$, so

$$
v=1.045\times1.55=1.62\ \text{m/s}
$$

Since 1.62 m/s is greater than the self-cleansing velocity of 0.6 m/s, the sewer does maintain the self-cleansing velocity when the flow drops to 0.6 m³/s.

**Answer: D = 0.907 m, full velocity = 1.55 m/s; at 0.6 m³/s the depth is about 0.56D and the velocity is 1.62 m/s, so self-cleansing is maintained.**

## Check yourself

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

1. Computed D for Q = 1 m3/s, S = 1/400, n = 0.012 is 0.907 m. Which formula is used?
   A. D = (Q n S^(1/2) / 0.3117)^(3/8)
   B. D = (Q n / (0.3117 S^(1/2)))^(3/8)
   C. D = (Q / 0.3117)^(1/2)
   D. D = (0.3117 Q / (n S^(1/2)))^(3/8)
   Answer: B. It is the inversion of Q_f = (0.3117/n) D^(8/3) S^(1/2). (Key point: Diameter running full)

2. How is the full velocity of 1.55 m/s obtained?
   A. v = Q / (pi/4 D^2)
   B. v = Q x D
   C. v = Q / D
   D. v = Q / (pi D^2)
   Answer: A. Continuity: velocity equals discharge divided by cross-sectional area. (Key point: Velocity just full)

3. For the dry-flow check, why is Q/Q_f computed with the adopted 1.05 m pipe?
   A. Because 0.907 m cannot be used in Manning's formula
   B. Because Q_f must be exactly 1 m3/s
   C. The actual sewer built is 1.05 m, so its Q_f = 1.479 m3/s is the reference for 0.6 m3/s
   D. Because the slope changes with the adopted size
   Answer: C. The check must be done on the real pipe: Q/Q_f = 0.6/1.479 = 0.4056. (Key point: Using adopted pipe)

4. At 0.6 m3/s the sewer velocity is 1.62 m/s. What is concluded?
   A. Below 0.6 m/s, so silting occurs
   B. Above 0.6 m/s, so self-cleansing velocity is maintained
   C. Equal to v_f so no check is needed
   D. Above 3 m/s so scour occurs
   Answer: B. v = 0.948 x 1.708 = 1.62 m/s, which exceeds the self-cleansing 0.6 m/s. (Key point: Self-cleansing at 0.6 m3/s)

## Related in Sanitary Engineering

- [Separate sewer, check self-cleansing](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Aseparate-sewer-0p5-self-cleansing) — Sanitary Engineering, chapter 3
- [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
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- [Combined sewer, half full, 1.5 m³/s](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-1p5-half-full) — Sanitary Engineering, chapter 3, asked 2×
- [Separate sewer, 0.70 full, 100000 persons](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-0p7-full-100000) — Sanitary Engineering, chapter 3, asked 2×
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