---
title: "Design discharge, separate and combined"
subject: "Sanitary Engineering"
chapter: 2
key: "semester_6/sanitary_engineering:design-discharge-separate-combined-45000"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/design-discharge-separate-combined-45000
site: BCT Engineering
---

# Design discharge, separate and combined

Sanitary Engineering · Chapter 2: Quantity of Wastewater

- Asked in: 2068 Magh (old course), 8 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/design-discharge-separate-combined-45000
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-2

## Question

Determine the design discharge for separate and combined systems of a small town with projected population of 45000 residing over an area of 20 hectares.
Rate of water supply = 150 lpcd; Runoff coefficient = 0.45; Time of concentration = 30 mins; Sewer slope = 1 in 500; Manning's n = 0.013.

## Short answer

Separate system sewage flow is 0.1875 m3/s, requiring about a 0.525 m sewer at slope 1 in 500. Combined system adds storm flow 0.475 m3/s, giving 0.662 m3/s and about a 0.90 m sewer.

## Answer

#### Assumptions
- 80% of water supplied becomes sewage; peak factor = 3; infiltration neglected.
- No rainfall formula is given, so $i=\dfrac{760}{t+10}$ mm/hr is assumed for the intensity at $t_c$.

#### (a) Separate system (sewage only)
$$
Q_{sew}=\frac{45000\times150\times0.8\times3}{86400\times1000}=0.1875\ \text{m}^3/\text{s}=187.5\ \text{l/s}
$$

Design the sewer running full ($S=1/500$, $n=0.013$). From Manning's formula for a full circular pipe, $Q=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$:

$$
D=\left(\frac{Q\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{0.1875\times0.013}{0.3117\times0.04472}\right)^{3/8}=0.520\ \text{m}
$$

Adopt $D=0.525$ m (standard size). Full velocity $v=\dfrac{0.3969}{n}D^{2/3}S^{1/2}=0.89$ m/s, which is above 0.6 m/s.

#### (b) Combined system
$$
\begin{aligned}
i&=\frac{760}{30+10}=19.0\ \text{mm/hr}\\
Q_{storm}&=\frac{0.45\times19.0\times20}{360}=0.475\ \text{m}^3/\text{s}\\
Q_{comb}&=Q_{sew}+Q_{storm}=0.1875+0.475=0.662\ \text{m}^3/\text{s}
\end{aligned}
$$

$$
D=\left(\frac{0.662\times0.013}{0.3117\times0.04472}\right)^{3/8}=0.835\ \text{m}
$$

Adopt $D=0.90$ m. Full velocity $=1.27$ m/s (below the 3 m/s maximum).

**Answer:** Separate system: $Q=0.1875$ m³/s, sewer about $D=0.525$ m. Combined system: $Q=0.662$ m³/s, sewer about $D=0.90$ m, both at slope 1 in 500.

## Check yourself

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

1. Design discharge of the separate system (45000, 150 lpcd, 80%, PF 3) is
   A. 0.0625 m3/s
   B. 1.875 m3/s
   C. 0.1875 m3/s
   D. 0.475 m3/s
   Answer: C. 45000 x 150 x 0.8 x 3 / 86400000 = 0.1875 m3/s. (Key point: Separate system flow)

2. How is the combined design discharge obtained?
   A. Only the storm runoff 0.475 m3/s
   B. Sewage times storm
   C. Sewage only
   D. Sewage plus storm runoff, 0.1875 + 0.475 = 0.662 m3/s
   Answer: D. Storm = 0.45 x 19 x 20 / 360 = 0.475 m3/s. (Key point: Combined system)

3. Which relation is used to find the full-flowing circular sewer diameter?
   A. Manning's formula Q = (0.3117/n) D^(8/3) S^(1/2)
   B. Rational formula
   C. Harman's formula
   D. Q = P q / 86400
   Answer: A. D is obtained by solving Manning's formula for D. (Key point: Pipe diameter)

4. Compared with the separate sewer (D about 0.525 m), the combined sewer at the same slope is
   A. smaller
   B. larger, about 0.90 m
   C. the same
   D. not possible to size
   Answer: B. Storm flow makes the combined sewer much bigger; velocity is checked to be at least 0.6 m/s. (Key point: Result comparison)

## Related in Sanitary Engineering

- [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
- [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 vs combined sewerage systems](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Aseparate-vs-combined-sewerage) — Sanitary Engineering, chapter 1, asked 4×
- [Runoff from a 20 ha built-up area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Arunoff-builtup-area-20ha) — Sanitary Engineering, chapter 2
- [Combined sewer section, 85 ha area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-85ha) — Sanitary Engineering, chapter 3
- [Storm water from a 45 ha catchment](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Astorm-water-catchment-surfaces) — Sanitary Engineering, chapter 2

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