---
title: "Economical lined channel: Q 20"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:lined-canal-q20-slope-30cm-km"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/lined-canal-q20-slope-30cm-km
site: BCT Engineering
---

# Economical lined channel: Q 20

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2074 Bhadra, 6 marks
- Video: [4.8 Design of Lined Canal](https://www.youtube.com/watch?v=qXW1OrFAz78) — Sanjay Bonkile
- 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-q20-slope-30cm-km
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Design an economical trapezoidal lined channel to carry a discharge of 20 cumecs at a slope of 30 cm/km. The side slope of the channel is 1.5:1. The value of Manning's rugosity coefficient is 0.017 and limiting velocity in the channel is 1.5 m/s.

## Short answer

Most economical section with side slope 1.5H:1V gives depth 2.75 m, bed width 1.66 m. Velocity 1.26 m/s is below the limiting 1.5 m/s. Provide freeboard and lining.

## Answer

Given: $Q = 20\ \text{m}^3/\text{s}$, $S = 0.000300$ (1 in 3333), $n = 0.017$, side slope 1.5H:1V, limiting velocity 1.5 m/s. Slope 30 cm/km $= 0.0003$.

#### Most economical (best hydraulic) section

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

$$
B = 2D(\sqrt{1+1.5^2} - 1.5) = 0.6056D,\qquad A = D^2\left(2\sqrt{1+z^2} - z\right) = 2.1056D^2
$$

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

$$
Q = \frac{1}{n}\,2.1056D^2\left(\frac{D}{2}\right)^{2/3}S^{1/2} \Rightarrow D^{8/3} = \frac{Q n\,2^{2/3}}{2.1056\sqrt{S}}
$$

$$
D = 2.747\ \text{m},\quad B = 1.663\ \text{m},\quad A = 15.89\ \text{m}^2,\quad R = 1.373\ \text{m},\quad V = 1.259\ \text{m/s}
$$

Velocity 1.26 m/s is within the limiting velocity of 1.5 m/s.

**Answer:** Full supply depth $D \approx 2.75$ m, bed width $B \approx 1.66$ m, side slope 1.5H:1V, $V \approx 1.26$ 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. What is the slope 30 cm/km as a decimal?
   A. 0.003
   B. 0.03
   C. 0.00003
   D. 0.0003
   Answer: D. 0.3 m per 1000 m. (Key point: Slope)

2. What are B and A in terms of D for z = 1.5?
   A. B = 0.6056 D, A = 2.1056 D^2
   B. B = 1.2361 D, A = 1.7361 D^2
   C. B = 2D, A = 3.5 D^2
   D. B = 0.5D, A = 1.5 D^2
   Answer: A. B = 2D(sqrt(3.25) - 1.5). (Key point: Best section)

3. Why is the best section accepted?
   A. V = 1.26 m/s exceeds 1.5 m/s
   B. V = 1.26 m/s is below the limiting 1.5 m/s
   C. V equals 1.5 m/s exactly
   D. The limit applies only to unlined channels
   Answer: B. The limit is not exceeded, so no adjustment is needed. (Key point: Velocity check)

4. What are D and B?
   A. D about 1.66 m, B about 2.75 m
   B. D about 2.75 m, B about 16.6 m
   C. D about 2.75 m, B about 1.66 m
   D. D about 1.37 m, B about 1.66 m
   Answer: C. From D^(8/3) = Q n 2^(2/3)/(2.1056 sqrt S). (Key point: Result)

## Related in Irrigation and Drainage Engineering

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