---
title: "Concrete-lined canal: Q 70, slope 1 in 4000"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:lined-canal-slope-14000-q70"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/lined-canal-slope-14000-q70
site: BCT Engineering
---

# Concrete-lined canal: Q 70, slope 1 in 4000

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2078 Poush, 7 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/lined-canal-slope-14000-q70
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

A concrete lined canal has a bed slope of 1 in 4000, carries the discharge of 70 cumecs. Side slope of canal is ½:1 (H:V), calculate dimension of the canal section.

## Short answer

For most economical trapezoidal section, depth 4.66 m, bed width 5.76 m, side slope 0.5H:1V, velocity 1.85 m/s.

## Answer

Given: $Q = 70\ \text{m}^3/\text{s}$, $S = 0.000250$ (1 in 4000), $n = 0.015$, side slope 0.5H:1V. Manning's $n$ is not given; $n = 0.015$ for concrete lining is assumed.

#### Most economical (best hydraulic) section

For a trapezoidal section of least perimeter: $R = D/2$ and $B = 2D(\sqrt{1+z^2} - z)$.

$$
B = 2D(\sqrt{1+0.5^2} - 0.5) = 1.2361D,\qquad A = D^2\left(2\sqrt{1+z^2} - z\right) = 1.7361D^2
$$

Using Manning's equation with $R = D/2$:

$$
Q = \frac{1}{n}\,1.7361D^2\left(\frac{D}{2}\right)^{2/3}S^{1/2} \Rightarrow D^{8/3} = \frac{Q n\,2^{2/3}}{1.7361\sqrt{S}}
$$

$$
D = 4.664\ \text{m},\quad B = 5.765\ \text{m},\quad A = 37.76\ \text{m}^2,\quad R = 2.332\ \text{m},\quad V = 1.854\ \text{m/s}
$$

The velocity is within the safe limit for concrete lining (about 2.5 m/s).

**Answer:** Full supply depth $D \approx 4.66$ m, bed width $B \approx 5.76$ m, side slope 0.5H:1V, $V \approx 1.85$ m/s. Add freeboard (0.5-0.75 m) and lining thickness as required.

## Check yourself

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

1. Manning's n is not given. What is used and why?
   A. n = 0.025 for earth
   B. n = 0.015 for concrete lining
   C. n = 0.0225 for gravel
   D. n = 0.035 for weeds
   Answer: B. The canal is concrete-lined. (Key point: Assumed n)

2. What relations define the economical section for z = 0.5?
   A. R = D, B = D, A = 1.5 D^2
   B. R = D/2, B = 2D, A = 2 D^2
   C. R = D/2, B = 1.2361 D, A = 1.7361 D^2
   D. R = D/3, B = 0.5 D, A = D^2
   Answer: C. B = 2D(sqrt(1.25) - 0.5) = 1.2361 D. (Key point: Best section)

3. What is the final design?
   A. D about 5.76 m, B about 4.66 m
   B. D about 2.33 m, B about 2.9 m
   C. D about 4.66 m, B about 1.2 m
   D. D about 4.66 m, B about 5.76 m, V about 1.85 m/s
   Answer: D. Manning with R = D/2 gives D^(8/3) from Q, n and S. (Key point: Result)

## Related in Irrigation and Drainage Engineering

- [Concrete-lined canal: Q 45, 45° slopes](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alined-canal-q45-slope-17000) — Irrigation and Drainage Engineering, chapter 4
- [Concrete-lined canal: Q 350](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alined-canal-q350-slope-15000) — Irrigation and Drainage Engineering, chapter 4
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## Related in other subjects

- [Economical channel: unlined versus concrete lined](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aeconomical-trapezoidal-unlined-vs-lined) — Hydraulics, chapter 6, asked 2×
- [Economical rectangular condition and trapezoidal bed slope](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atrapezoidal-channel-bed-slope) — Hydro Power, chapter 1
- [Canal earthwork, bed 3 m, free board 0.44 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Achannel-q-portion) — Estimating and Costing, chapter 6
- [Increase in discharge after lining the bed](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aconcrete-lining-increase-in-discharge) — Hydraulics, chapter 6