---
title: "Design discharge from given data"
subject: "Sanitary Engineering"
chapter: 2
key: "semester_6/sanitary_engineering:design-discharge-sewer-75000"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/design-discharge-sewer-75000
site: BCT Engineering
---

# Design discharge from given data

Sanitary Engineering · Chapter 2: Quantity of Wastewater

- Asked in: 2072 Asoj, 4 marks
- Video: [calculation of discharge of sewage in combined sewage sysytem | Environmental Engineering numerical](https://www.youtube.com/watch?v=dLrq2au_uLQ) — 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-sewer-75000
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-2

## Question

Calculate the design discharge for a sewer from the following data:
Projected population = 75,000
Area = 8 km²
Rate of w/s = 100 lpcd
Permeability factor = 60%
Rainfall duration = 15 minutes
Time of flow = 15 minutes
Time of entry = 5 minutes
Assume that 80% supplied water converted as wastewater and maximum demand is 3 times average demand.

## Short answer

Peak sewage is 0.2083 m3/s using 80 lpcd and peak factor 3. Storm runoff with C=0.40, i=30.4 mm/hr, A=800 ha is 27.022 m3/s. Total design discharge is 27.231 m3/s.

## Answer

The design discharge of a combined sewer is the peak sanitary sewage plus the storm water runoff.

#### Assumptions
- Permeability 60% means the area is 40% impervious, so $C=1-0.60=0.40$.
- Rainfall intensity for the given storm duration of 15 min is taken from $i=\dfrac{760}{t+10}$ mm/hr (assumed empirical formula, $t$ in min).
- Time of concentration $t_c=t_e+t_f=5+15=20$ min (the storm of 15 min is used for intensity as given).

#### Step 1: Sanitary sewage
Average sewage = 80% of 100 lpcd = 80 lpcd. Peak = 3 x average.

$$
Q_{sewage}=\frac{75000\times100\times0.8\times3}{86400\times1000}=0.2083\ \text{m}^3/\text{s}
$$

#### Step 2: Storm water
Area $A=8\ \text{km}^2=800$ ha.

$$
\begin{aligned}
i&=\frac{760}{15+10}=30.40\ \text{mm/hr}\\
Q_{storm}&=\frac{C\,i\,A}{360}=\frac{0.40\times30.40\times800}{360}=27.022\ \text{m}^3/\text{s}
\end{aligned}
$$

#### Step 3: Design discharge
$$
Q=Q_{sewage}+Q_{storm}=0.2083+27.022=27.231\ \text{m}^3/\text{s}
$$

**Answer: Design discharge = 27.231 m³/s** (storm water 27.022 m³/s plus sewage 0.2083 m³/s). If the examination supplies its own intensity formula, replace $i$ and the same steps apply.

## Check yourself

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

1. A permeability of 60% gives a runoff coefficient of
   A. 0.60
   B. 0.40
   C. 1.60
   D. 0.06
   Answer: B. Impervious fraction = 1 - 0.60 = 0.40. (Key point: Permeability to C)

2. Peak sewage flow here is
   A. 0.0694 m3/s
   B. 2.083 m3/s
   C. 0.2083 m3/s
   D. 0.625 m3/s
   Answer: C. 75000 x 100 x 0.8 x 3 / (86400 x 1000) = 0.2083 m3/s. (Key point: Sewage flow)

3. The 8 km2 area in hectares is
   A. 80 ha
   B. 8000 ha
   C. 8 ha
   D. 800 ha
   Answer: D. 1 km2 = 100 ha. (Key point: Area conversion)

4. The design discharge is the sum of
   A. sewage and storm water, about 0.208 + 27.022 = 27.231 m3/s
   B. storm water only
   C. sewage x storm water
   D. average sewage and infiltration
   Answer: A. For a combined sewer it is peak sewage plus storm runoff. (Key point: Design discharge)

## Related in Sanitary Engineering

- [Sewer diameter for a 2.5 sq km area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-diameter-2p5-sqkm) — 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 for a 12 sq km area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-diameter-12-sqkm) — 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
- [Minimum sewer diameter, 80000 population](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Asewer-min-diameter-80000) — 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

## 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
- [Design pipes AB and BC, 75 lpcd, tank 6 m high](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-b81) — Water Supply Engineering, chapter 7
- [Design pipes AB, BC; 160 lpcd, peak factor 3](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apd-c71) — Water Supply Engineering, chapter 7