---
title: "Concrete-lined canal: Q 45, 45° slopes"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:lined-canal-q45-slope-17000"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/lined-canal-q45-slope-17000
site: BCT Engineering
---

# Concrete-lined canal: Q 45, 45° slopes

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2075 Bhadra, 8 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-q45-slope-17000
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Design concrete lined canal to carry a discharge of 45 cumec. The bed slope of canal is assumed to be 1 in 7000. Take side slope of canal as 45° and Manning coefficient is 0.015.

## Short answer

For most economical trapezoidal section with side slope 1H:1V, Manning’s equation yields depth 4.30 m, bed width 3.57 m. Velocity 1.33 m/s is safe for concrete lining. Add freeboard and lining thickness.

## Answer

Given: $Q = 45\ \text{m}^3/\text{s}$, $S = 0.000143$ (1 in 7000), $n = 0.015$, side slope 1H:1V. A side slope of 45° means 1H:1V.

#### Most economical (best hydraulic) section

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

$$
B = 2D(\sqrt{1+1^2} - 1) = 0.8284D,\qquad A = D^2\left(2\sqrt{1+z^2} - z\right) = 1.8284D^2
$$

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

$$
Q = \frac{1}{n}\,1.8284D^2\left(\frac{D}{2}\right)^{2/3}S^{1/2} \Rightarrow D^{8/3} = \frac{Q n\,2^{2/3}}{1.8284\sqrt{S}}
$$

$$
D = 4.305\ \text{m},\quad B = 3.566\ \text{m},\quad A = 33.88\ \text{m}^2,\quad R = 2.152\ \text{m},\quad V = 1.328\ \text{m/s}
$$

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

**Answer:** Full supply depth $D \approx 4.30$ m, bed width $B \approx 3.57$ m, side slope 1H:1V, $V \approx 1.33$ 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 side slope does 45 degrees represent?
   A. 0.5H:1V
   B. 1H:1V
   C. 1.5H:1V
   D. 2H:1V
   Answer: B. tan 45 = 1 so horizontal equals vertical. (Key point: Side slope)

2. For z = 1, what are B and A in terms of D?
   A. B = 2D, A = 3D^2
   B. B = 1.2361 D, A = 1.7361 D^2
   C. B = 0.8284 D, A = 1.8284 D^2
   D. B = 0.5 D, A = D^2
   Answer: C. B = 2D(sqrt2 - 1) and A = D^2(2 sqrt2 - 1). (Key point: Best section)

3. How is D found?
   A. Use Lacey's P = 4.75 sqrt(Q)
   B. Use tau_c = gamma D S
   C. Use V = 0.55 D^0.64
   D. Substitute R = D/2 into Manning: D^(8/3) = Q n 2^(2/3)/(1.8284 sqrt S)
   Answer: D. This gives D = 4.30 m. (Key point: Using Manning)

4. What are the final dimensions?
   A. D about 4.30 m, B about 3.57 m, V about 1.33 m/s
   B. D about 3.57 m, B about 4.30 m
   C. D about 4.30 m, B about 8.6 m
   D. D about 2.15 m, B about 3.57 m
   Answer: A. V = 1.33 m/s is within the 2.5 m/s limit for concrete. (Key point: Result)

## Related in Irrigation and Drainage Engineering

- [Concrete-lined canal: Q 70, slope 1 in 4000](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alined-canal-slope-14000-q70) — 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
- [Lined canal capacity and irrigable area](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alined-canal-trapezoid-5m-bed-capacity) — Irrigation and Drainage Engineering, chapter 4, asked 2×
- [Cross drainage: Q 40, 45 cumec drainage](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acd-q40-bed30-fsd16-syphonic) — Irrigation and Drainage Engineering, chapter 8
- [Economical lined channel: Q 20](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alined-canal-q20-slope-30cm-km) — Irrigation and Drainage Engineering, chapter 4
- [Tractive force design: Q 45](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Atractive-q45-slope-14500) — Irrigation and Drainage Engineering, chapter 4, asked 3×

## 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×
- [Efficient trapezoid with unequal side slopes](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Aefficient-trapezoidal-two-side-slopes-critical-depth) — Hydraulics, 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
- [Canal slope stability: HS 138/45](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Acanal-slope-stability-hs138-45) — Engineering Geology II, chapter 6