---
title: "Combined circular sewer, 35 ha"
subject: "Sanitary Engineering"
chapter: 3
key: "semester_6/sanitary_engineering:combined-sewer-35ha"
source: https://www.bctengineer.com/q/semester_6/sanitary_engineering/combined-sewer-35ha
site: BCT Engineering
---

# Combined circular sewer, 35 ha

Sanitary Engineering · Chapter 3: Design and Construction of Sewers

- Asked in: 2070 Magh, 8 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/combined-sewer-35ha
- Whole chapter: https://www.bctengineer.com/md/semester_6/sanitary_engineering/chapter-3

## Question

Calculate the diameter of combined circular sewer with following data: water supply rate = 100 lpcd, population density = 100 persons/hec, peak factor = 2.7, area = 35 hectares, rainfall intensity = 15 mm/hr, slope = 1/750, Manning's coefficient of rugosity = 0.011. The coefficient of run-off = 0.4. The sewer should run 0.6 depth full during peak flow.

## Short answer

Combined Q=0.5921 m³/s at d/D=0.6. Using proportional relations, Q_f=0.8813 m³/s; Manning's with n=0.011, S=1/750 gives D=0.942 m. Provide 1050 mm pipe, resulting v=1.46 m/s (between 0.6 and 3.0 m/s, acceptable).

## Answer

#### Step 1: Sewage flow
Population $=100\times35=3500$. Assume 80% of the supply becomes sewage.

$$
Q_{sew}=\frac{3500\times100\times0.8\times2.7}{86400\times1000}=0.00875\ \text{m}^3/\text{s}
$$

#### Step 2: Storm water
$$
Q_{storm}=\frac{C\,i\,A}{360}=\frac{0.4\times15\times35}{360}=0.5833\ \text{m}^3/\text{s}
$$

#### Step 3: Combined design discharge
$$
Q=0.00875+0.5833=0.5921\ \text{m}^3/\text{s}
$$

#### Step 4: Diameter ($d/D=0.6$, $S=1/750$, $n=0.011$)
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:

$$
Q_f=\frac{Q}{Q/Q_f}=\frac{0.5921}{0.6718}=0.8813\ \text{m}^3/\text{s}
$$

Manning's formula for a full circular pipe, $Q_f=\dfrac{0.3117}{n}D^{8/3}S^{1/2}$, with $S=0.00133$ and $n=0.011$:

$$
D=\left(\frac{Q_f\,n}{0.3117\,S^{1/2}}\right)^{3/8}=\left(\frac{0.8813\times0.011}{0.3117\times0.03651}\right)^{3/8}=0.942\ \text{m}
$$

Adopt the next standard size, **D = 1050 mm**.

#### Check of velocity and capacity
For the adopted pipe: $v_f=\dfrac{0.3969}{n}D^{2/3}S^{1/2}=1.361$ m/s and $Q_f=1.1785$ m³/s.

$$
\begin{aligned}
v&=v_f\times(v/v_f)=1.361\times1.0724=1.46\ \text{m/s}\\
Q_{capacity}&=Q_f\times(Q/Q_f)=1.1785\times0.6718=0.7917\ \text{m}^3/\text{s}\ (\ge 0.5921)
\end{aligned}
$$

The velocity at maximum flow, 1.46 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: Diameter of the combined circular sewer = 0.942 m; provide 1050 mm.**

## Check yourself

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

1. With 100 persons/ha on 35 ha, the sewage peak flow is mainly small because
   A. Population is only 3500, giving Q = 0.00875 m3/s versus 0.583 m3/s of storm water
   B. Peak factor is below 1
   C. Water supply is zero
   D. Sewage is ignored in combined sewers
   Answer: A. 3500 x 100 x 0.8 x 2.7 / 86400000 = 0.00875 m3/s. (Key point: Sewage flow)

2. Which gives the storm flow when i = 15 mm/hr?
   A. Q = C i A x 360
   B. Q = C i A / 360 = 0.4 x 15 x 35 / 360 = 0.583 m3/s
   C. Q = C i A / 3600
   D. Q = i A / C
   Answer: B. Rational formula with i in mm/hr and A in ha. (Key point: Storm water flow)

3. With the sewer 0.6 deep at peak flow, the required Q_f is
   A. 0.5921 x 0.6718
   B. 0.5921 m3/s
   C. 0.5921/0.6718 = 0.881 m3/s
   D. 0.5921/0.6 = 0.987 m3/s
   Answer: C. Q/Q_f = 0.6718 at d/D = 0.6, so Q_f = Q divided by that ratio. (Key point: Required full discharge)

4. The computed D and adopted size are
   A. 1.05 m and 942 mm
   B. 0.6 m and 600 mm
   C. 1.2 m and 1200 mm
   D. 0.942 m and 1050 mm
   Answer: D. D computed with n = 0.011 and S = 1/750, then next standard size 1050 mm adopted; v = 1.46 m/s. (Key point: Final diameter)

## Related in Sanitary Engineering

- [Circular combined sewer, 60 ha](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-60ha) — Sanitary Engineering, chapter 3
- [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
- [Combined sewer section, 85 ha area](https://www.bctengineer.com/question.md?key=semester_6%2Fsanitary_engineering%3Acombined-sewer-85ha) — 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
- [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
- [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

## 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, 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
- [Population 2090 by three methods, 110 lpcd](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Apop-b79) — Water Supply Engineering, chapter 3, asked 2×
- [Balancing reservoir: village 600 population, 65 lpcd](https://www.bctengineer.com/question.md?key=semester_5%2Fwater_supply_engineering%3Ares-as70) — Water Supply Engineering, chapter 7