---
title: "Separate sewer, 0.6 full, 250000 persons"
subject: "Sanitary Engineering"
chapter: 3
key: "semester_6/sanitary_engineering:sewer-0p6-full-250000"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/sewer-0p6-full-250000
site: BCT Engineering
---

# Separate sewer, 0.6 full, 250000 persons

Sanitary Engineering · Chapter 3: Design and Construction of Sewers

- Asked in: 2081 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-0p6-full-250000
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3

## Question

Design a sewer running 0.6 times full at maximum discharge for a town provided with the separate system serving a population of 250,000 persons. Water is from the water-work at a rate of 200 lpcd. Take a constant value of n = 0.013 at all depths of flow. The permissible slope is 1 in 600. Take peak factor of 2.25.

## Short answer

Design flow = (250000×200×0.8×2.25)/(86400×1000) = 1.0417 m³/s. With Q/Q_f=0.6718 at 0.6 depth, Q_f=1.5505 m³/s; from Manning's, D=1.188 m (adopt 1200 mm). At slope 1 in 600, velocity = 1.51 m/s.

## Answer

#### Design flow
Assume 80% of the water supplied reaches the sewer. Peak factor = 2.25.

$$
Q_{max}=\frac{250000\times200\times0.8\times2.25}{86400\times1000}=1.0417\ \text{m}^3/\text{s}
$$

Data: $S=1/600$, $n=0.013$ (constant), depth ratio $d/D=0.6$.

For $d/D=0.6$: $\theta = 2\cos^{-1}(1-2d/D)=203.07^\circ$, $A/A_f=\dfrac{\theta-\sin\theta}{2\pi}=0.6265$, $R/R_f=1-\dfrac{\sin\theta}{\theta}=1.1106$, so $v/v_f=(R/R_f)^{2/3}=1.0724$ and $Q/Q_f=(A/A_f)(v/v_f)=0.6718$ (n taken constant).

#### Size of the sewer
Discharge when running full:

$$
Q_f=\frac{Q}{Q/Q_f}=\frac{1.0417}{0.6718}=1.5505\ \text{m}^3/\text{s}
$$

Manning's formula for a full circular pipe, $Q_f=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$, with $S=0.00167$ and $n=0.013$:

$$
D=\left(\frac{Q_f\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{1.5505\times0.013}{0.3117\times0.04082}\right)^{3/8}=1.188\ \text{m}
$$

Adopt the next standard size, **D = 1200 mm**.

#### Check of velocity and capacity
For the adopted pipe: $v_f=\dfrac{0.3969}{n}D^{2/3}S^{1/2}=1.408$ m/s and $Q_f=1.5917$ m³/s.

$$
\begin{aligned}
v&=v_f\times(v/v_f)=1.408\times1.0724=1.51\ \text{m/s}\\
Q_{capacity}&=Q_f\times(Q/Q_f)=1.5917\times0.6718=1.0694\ \text{m}^3/\text{s}\ (\ge 1.0417)
\end{aligned}
$$

The velocity at maximum flow, 1.51 m/s, lies between the minimum (0.6 m/s) and the maximum non-scouring limit (3.0 m/s), so it is satisfactory.

**Answer: Provide a circular sewer of D = 1200 mm at slope 1 in 600; it runs 0.6 full with v = 1.51 m/s at Q = 1.0417 m³/s** (computed diameter 1.188 m). Such a large flow may also be carried by two parallel sewers.

## Check yourself

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

1. Which expression gives the maximum sewage flow here?
   A. Population x per capita supply x peak factor / 86400 only, with no sewage fraction
   B. Population x per capita supply x 0.8 x peak factor / (86400 x 1000)
   C. Population x supply x 0.8 / (3600 x 1000)
   D. Population x supply x 0.8 / peak factor / 86400000
   Answer: B. 80% of the water supplied is assumed to reach the sewer, then multiplied by the peak factor and converted to m3/s: 1.0417 m3/s. (Key point: Design flow)

2. At d/D = 0.6 with constant n, Q/Q_f is
   A. 0.6265
   B. 1.0724
   C. 0.6718
   D. 0.6
   Answer: C. Q/Q_f = (A/A_f)(v/v_f) = 0.6265 x 1.0724 = 0.6718. (Key point: Discharge ratio at 0.6 depth)

3. What full discharge is used in Manning's formula and what D results?
   A. Q_f = 1.0417/0.6718 = 1.55 m3/s giving D = 1.188 m
   B. Q_f = 1.0417 m3/s giving D = 1.0 m
   C. Q_f = 1.0417 x 0.6718 giving D = 0.9 m
   D. Q_f = 1.55 m3/s giving D = 2.4 m
   Answer: A. Dividing by the ratio gives Q_f, then D = (Q_f n/(0.3117 S^0.5))^(3/8) = 1.188 m; adopt 1200 mm. (Key point: Full discharge and diameter)

4. Why is the 1200 mm pipe satisfactory?
   A. Its capacity is less than demand but velocity is high
   B. Capacity 1.069 m3/s exceeds 1.0417 and velocity 1.51 m/s is between 0.6 and 3.0 m/s
   C. Velocity of 1.51 m/s exceeds 3 m/s which is desirable
   D. Only the computed diameter 1.188 m is satisfactory
   Answer: B. Both capacity and velocity limits must be met after adopting the standard size. (Key point: Check of adopted pipe)

## Close variants set in other exams

- [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×

## Related in Sanitary Engineering

- [Design discharge, separate and combined](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Adesign-discharge-separate-combined-45000) — Sanitary Engineering, chapter 2
- [Minimum sewer diameter, 80000 population](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-min-diameter-80000) — 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
- [Design discharge from given data](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Adesign-discharge-sewer-75000) — Sanitary Engineering, chapter 2
- [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
- [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

## Related in other subjects

- [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, 20,000 population, f = 0.04](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-b66) — Water Supply Engineering, chapter 7
- [Geological work of running water and its landforms](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Ageological-work-of-running-water) — Engineering Geology I, chapter 6, asked 5×