---
title: "Draw balanced canal section"
subject: "Estimating and Costing"
chapter: 6
key: "semester_7/estimating_and_costing:balanced-canal-section-draw"
source: https://www.bctengineer.com/q/semester_7/estimating_and_costing/balanced-canal-section-draw
site: BCT Engineering
---

# Draw balanced canal section

Estimating and Costing · Chapter 6: Detailed Estimate

- Asked in: 2080 Bhadra, 2 marks
- Video: [find balance depth | irrigation numerical | 2022  PU | cutting and filling](https://www.youtube.com/watch?v=1jTPF0D5fPY) — Sudip Dhakal
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_7/estimating_and_costing/balanced-canal-section-draw
- Whole chapter: https://www.bctengineer.com/md/semester_7/estimating_and_costing/chapter-6

## Question

Draw a balanced canal section.

## Short answer

A balanced canal section is one where excavation equals embankment, with no surplus or borrow. The balancing depth satisfies (b+sd)d = 2(t+s hb)hb, equating cut area to bank area.

## Answer

A **balanced section** is a canal section partly in cutting and partly in banking in which the earth excavated from the bed is exactly enough to build the banks, so there is no surplus spoil and no earth is borrowed. The depth of cutting at which this happens is the **balancing depth**.

```text
 bank top ______                    ______
         /      \                  /      \
        /  bank  \  F.S.L ~~~~~~~/  bank  \
 G.L ===/          \            /          \===
                    \          /
                     \________/
                      bed width b
```

Condition: area of cutting below ground = area of the two banks above ground.

$$
(b + s\,d)\,d = 2\,(t + s\,h_b)\,h_b,\qquad h_b = D - d
$$

where $d$ is the depth of cutting, $D$ = full supply depth + free board, $t$ = top width of one bank and $s$ the side slope.

Example (assumed $b = 5$ m, $s = 1.5$, $t = 2$ m, $D = 1.6$ m): solving gives $d = 0.810$ m, cutting area $= 5.033$ m² and bank area $= 5.033$ m² (equal).

## Check yourself

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

1. A balanced section of a canal is one in which:
   A. Bed width equals depth
   B. Excavated earth exactly suffices to form the banks, with no surplus or borrowing
   C. The canal is entirely in banking
   D. Both banks have the same top width only
   Answer: B. Cutting from the bed provides exactly the earth needed for the banks. (Key point: Balanced section definition)

2. The condition used to find the balancing depth is:
   A. Area of cutting below ground = area of the two banks above ground
   B. Depth of cutting = height of banks
   C. Bed width = top width of bank
   D. Full supply depth = free board
   Answer: A. Equal areas (hence equal volumes per unit length) of cutting and banking give (b + s d)d = 2(t + s h_b)h_b. (Key point: Balancing condition)

3. If D is full supply depth plus free board and d is the depth of cutting, the bank height above ground is:
   A. h_b = D + d
   B. h_b = D - d
   C. h_b = d - D
   D. h_b = D x d
   Answer: B. The total depth D is partly below ground (d) and the rest (D - d) is above ground as bank. (Key point: Bank height)

## Related in Estimating and Costing

- [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
- [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

## Related in other subjects

- [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 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
- [Balanced, under, over sections with strain diagrams](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Abalanced-under-over-sections-with-strain) — Design of RCC Structure, 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×