---
title: "Balancing depth: bed width 20 m"
subject: "Irrigation and Drainage Engineering"
chapter: 3
key: "semester_6/irrigation_and_drainage_engineering:balancing-depth-bed20-cut15-fill2"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/balancing-depth-bed20-cut15-fill2
site: BCT Engineering
---

# Balancing depth: bed width 20 m

Irrigation and Drainage Engineering · Chapter 3: Canal Irrigation System

- Asked in: 2080 Chaitra, 4 marks; 2077 Chaitra, 2 marks (asked 2 times)
- 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-bed20-cut15-fill2
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-3

## Question

Calculate the balancing depth of an irrigation canal using the following data: Bed width of canal = 20 m; side slope of cutting = 1.5:1 (H:V); side slope of banking = 2:1 (H:V); top width of bank = 3 m; height of embankment = 4 m (bank embankments kept 4 m higher than the ground level (berm)).

## Short answer

Equate cut area (20+1.5d)d to fill area 2×4×(3+2×4)=88 m². Solve 1.5d²+20d-88=0 to get d = 3.49 m.

## Answer

**Given:** $B = 20$ m, cutting slope $n_1 = 1.5$ (H:V), banking slope $n_2 = 2$ (H:V), top width of bank $b = 3$ m, height of bank above ground $h = 4$ m. Both faces of each bank are taken at 2:1, and no berm is considered.

**Condition:** cutting area = filling area (two banks).

**Filling area** (both banks):

$$
A_f = 2h\,(b + n_2 h) = 2\times4\times(3 + 2\times4) = 88\ \text{m}^2
$$

**Cutting area:**

$$
A_c = (B + n_1 d)\,d = (20 + 1.5d)\,d
$$

**Equate:**

$$
1.5d^2 + 20d - 88 = 0
$$

$$
d = \frac{-20 + \sqrt{20^2 + 4\times1.5\times88}}{2\times1.5} = \frac{-20+\sqrt{928}}{3} = 3.488\ \text{m}
$$

**Check:** $A_c = (20+1.5\times3.488)3.488 = 88.00$ m$^2$, equal to $A_f = 88$ m$^2$.

**Answer: balancing depth = 3.49 m.**

## Check yourself

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

1. What is the filling area for both banks (b=3, h=4, n2=2)?
   A. 88 m^2
   B. 44 m^2
   C. 56 m^2
   D. 176 m^2
   Answer: A. 2 x 4 x (3 + 8) = 88 m^2. (Key point: Filling area)

2. Which equation results from equating cut and fill?
   A. 1.5 d^2 + 20 d + 88 = 0
   B. 1.5 d^2 + 20 d - 88 = 0
   C. 2 d^2 + 20 d - 88 = 0
   D. 1.5 d^2 - 20 d - 88 = 0
   Answer: B. (20 + 1.5d)d = 88. (Key point: Equation)

3. What is the balancing depth?
   A. 4.0 m
   B. 2.93 m
   C. 3.49 m
   D. 5.87 m
   Answer: C. d = (-20 + sqrt(928))/3 = 3.488 m. (Key point: Balancing depth)

## Close variants set in other exams

- [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×

## Related in Irrigation and Drainage Engineering

- [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 and canal cross-section](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Abalancing-depth-bed8-section) — Irrigation and Drainage Engineering, chapter 3
- [Stable depth and bed width: Q 5, d50 3 cm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Astable-depth-bed-width-q5-d50) — Irrigation and Drainage Engineering, chapter 4
- [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×
- [Canal standards and balancing depth](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Acanal-standards-balancing-depth) — Irrigation and Drainage Engineering, chapter 3
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## Related in other subjects

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- [Hill road earthwork, cutting 4 m / banking 6 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Ahill-road-k-cut4-fill6) — Estimating and Costing, chapter 6
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