---
title: "Balancing depth: bed width 25 m"
subject: "Irrigation and Drainage Engineering"
chapter: 3
key: "semester_6/irrigation_and_drainage_engineering:balancing-depth-bed25"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/balancing-depth-bed25
site: BCT Engineering
---

# Balancing depth: bed width 25 m

Irrigation and Drainage Engineering · Chapter 3: Canal Irrigation System

- Asked in: 2081 Chaitra, 5 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-bed25
- 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 = 25 m; side slope of cutting = 1.75:1 (H:V); side slope of banking = 2.5:1 (H:V); top width of bank = 4 m; height of embankment = 5 m.

## Short answer

Equate cutting area (B + n1*d)*d to filling area 2*h*(b + n2*h). Solve quadratic 1.75d² + 25d - 165 = 0. Balancing depth = 4.91 m.

## Answer

**Given:** $B = 25$ m, $n_1 = 1.75$ (cutting), $n_2 = 2.5$ (banking), $b = 4$ m, $h = 5$ m. Both banks are built with slope 2.5:1 on both faces; no berm.

**Filling area** (two banks):

$$
A_f = 2h\,(b + n_2 h) = 2\times5\times(4+2.5\times5) = 165\ \text{m}^2
$$

**Cutting area:** $A_c = (25 + 1.75d)\,d$

**Equate** $A_c = A_f$:

$$
1.75d^2 + 25d - 165 = 0
$$

$$
d = \frac{-25+\sqrt{25^2+4\times1.75\times165}}{2\times1.75} = \frac{-25+\sqrt{1780}}{3.5} = 4.911\ \text{m}
$$

**Check:** $A_c = 165.00$ m$^2$ = $A_f = 165$ m$^2$.

**Answer: balancing depth = 4.91 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=4, h=5, n2=2.5)?
   A. 165 m^2
   B. 82.5 m^2
   C. 110 m^2
   D. 330 m^2
   Answer: A. 2 x 5 x (4 + 12.5) = 165. (Key point: Filling area)

2. Which equation is solved?
   A. 1.75 d^2 + 25 d + 165 = 0
   B. 1.75 d^2 + 25 d - 165 = 0
   C. 2.5 d^2 + 25 d - 165 = 0
   D. 1.75 d^2 - 25 d - 165 = 0
   Answer: B. Cutting (25 + 1.75d)d equals 165. (Key point: Equation)

3. What is the balancing depth?
   A. 5.0 m
   B. 3.5 m
   C. 4.91 m
   D. 6.8 m
   Answer: C. d = (-25 + sqrt(1780))/3.5 = 4.911 m. (Key point: Result)

4. How is the result verified?
   A. Bank height equals d
   B. FSL equals ground
   C. Bed width equals d
   D. Cutting area at d equals filling area 165 m^2
   Answer: D. At d = 4.911, (25+1.75d)d = 165. (Key point: Check)

## Close variants set in other exams

- [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×

## 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
- [Crest width, cistern length of vertical drop, Q 1.55](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Avertical-drop-q155-drop075) — Irrigation and Drainage Engineering, chapter 7, asked 2×

## Related in other subjects

- [Irrigation canal earthwork, 0-600 m](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Airrigation-canal-k-drop) — Estimating and Costing, chapter 6
- [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
- [Irrigation canal earthwork with vertical drop](https://www.bctengineer.com/question.md?key=semester_7%2Festimating_and_costing%3Acanal-a-drop-0-400) — Estimating and Costing, 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