---
title: "Balancing depth and canal cross-section"
subject: "Irrigation and Drainage Engineering"
chapter: 3
key: "semester_6/irrigation_and_drainage_engineering:balancing-depth-bed8-section"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/balancing-depth-bed8-section
site: BCT Engineering
---

# Balancing depth and canal cross-section

Irrigation and Drainage Engineering · Chapter 3: Canal Irrigation System

- Asked in: 2072 Asoj, 3+2 marks
- Video: [Calculate the balancing depth for a channel section,,, Irrigation and flood managament.](https://www.youtube.com/watch?v=wL9x75ixoKM) — E.T.E. Suman
- 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/balancing-depth-bed8-section
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-3

## Question

An irrigation channel has a bottom width 8 m and side slopes of 1.5H:1V in cutting and 2H:1V in filling. The width of the crest of bank is 2 m and its height above the ground level is 3 m. Compute the balancing depth and draw a neat x-section of the canal illustrating the various dimensions and level it.

## Short answer

Equate cutting area (8+1.5d)*d to filling area 2*3*(2+2*3)=48 m². Solve quadratic 1.5d² + 8d - 48 = 0. Balancing depth = 3.59 m.

## Answer

**Given:** $B = 8$ m, $n_1 = 1.5$ (cutting), $n_2 = 2$ (filling), crest width $b = 2$ m, bank height above ground $h = 3$ m. Banks are on both sides with 2:1 slopes on both faces; no berm.

**Filling area:**

$$
A_f = 2h\,(b + n_2h) = 2\times3\times(2+2\times3) = 48\ \text{m}^2
$$

**Cutting area:** $A_c = (8 + 1.5d)\,d$

**Equate:**

$$
1.5d^2 + 8d - 48 = 0\;\Rightarrow\; d = \frac{-8+\sqrt{64+4\times1.5\times48}}{3} = \frac{-8+\sqrt{352}}{3} = 3.587\ \text{m}
$$

**Answer: balancing depth = 3.59 m.**

**Cross-section (level with the ground at 0.00):**

```text
      2.0 m                          2.0 m
   |---|                          |---|
 +3.00 ____                       ____ +3.00
      /    \                     /    \
 2:1 /      \  ground 0.00       /      \ 2:1
 ---/        \--             --/        \---
                \ 1.5:1  1.5:1/
                 \            /   depth 3.59 m
                  \__________/ -3.59
                     8.0 m bed
```

Bed level is 3.59 m below ground; crest of each bank is 3.0 m above ground; bed width 8 m; cutting slopes 1.5H:1V; bank slopes 2H:1V; crest width 2 m.

## Check yourself

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

1. What is the filling area (b=2, h=3, n2=2, two banks)?
   A. 48 m^2
   B. 24 m^2
   C. 30 m^2
   D. 96 m^2
   Answer: A. 2 x 3 x (2 + 6) = 48. (Key point: Filling area)

2. What equation results?
   A. 1.5 d^2 + 8 d + 48 = 0
   B. 1.5 d^2 + 8 d - 48 = 0
   C. 2 d^2 + 8 d - 48 = 0
   D. 1.5 d^2 - 8 d - 48 = 0
   Answer: B. (8 + 1.5d)d = 48. (Key point: Equation)

3. What is the balancing depth?
   A. 3.0 m
   B. 4.5 m
   C. 3.59 m
   D. 2.7 m
   Answer: C. d = (-8 + sqrt(352))/3 = 3.587 m. (Key point: Balancing depth)

4. With ground at 0.00, what are the levels of the bed and the bank crest?
   A. Bed at +3.59 m and crest at -3.00 m
   B. Bed at -3.00 m and crest at +3.59 m
   C. Bed at 0 and crest at +6.59 m
   D. Bed at -3.59 m and crest at +3.00 m
   Answer: D. Bed is d below ground, crest h = 3 m above ground. (Key point: Section levels)

## Related in Irrigation and Drainage Engineering

- [Canal cross-section in cutting and filling](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acanal-cross-section-cut-fill) — Irrigation and Drainage Engineering, chapter 3, asked 3×
- [Balancing depth with service bank and free board](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed8-service-bank) — Irrigation and Drainage Engineering, chapter 3
- [Balancing depth: bed width 20 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed20-cut15-fill2) — Irrigation and Drainage Engineering, chapter 3, asked 3×
- [Balancing depth: bed width 25 m](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed25) — Irrigation and Drainage Engineering, chapter 3, asked 3×
- [Vertical drop crest level and width, Q 30](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-crest-q30-fsl315) — Irrigation and Drainage Engineering, chapter 7
- [Derive the balancing depth of a canal](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-derive) — Irrigation and Drainage Engineering, chapter 3, asked 2×

## Related in other subjects

- [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
- [Irrigation channel earthwork, bed 5 m, 1 in 3000](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Airrigation-channel-j) — Estimating and Costing, chapter 6
- [Efficient rectangular section and triangular channel depth](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-channel-normal-depth-rect) — Hydro Power, chapter 1, asked 2×
- [Efficient trapezoidal section and triangular channel depth](https://www.bctengineer.com/question.md?key=semester_6%2Fhydro_power%3Atriangular-channel-normal-depth-trap) — Hydro Power, chapter 1, asked 2×