---
title: "Stable depth and bed width: Q 5, d50 3 cm"
subject: "Irrigation and Drainage Engineering"
chapter: 4
key: "semester_6/irrigation_and_drainage_engineering:stable-depth-bed-width-q5-d50"
source: https://www.bctengineer.com/q/semester_6/irrigation_and_drainage_engineering/stable-depth-bed-width-q5-d50
site: BCT Engineering
---

# Stable depth and bed width: Q 5, d50 3 cm

Irrigation and Drainage Engineering · Chapter 4: Design of Canals

- Asked in: 2071 Bhadra, 6 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/stable-depth-bed-width-q5-d50
- Whole chapter: https://www.bctengineer.com/md/semester_6/irrigation_and_drainage_engineering/chapter-4

## Question

Sides of an irrigation canal with the following design parameters are well protected. What will be the stable depth and bed width of such a canal? Q = 5 m³/s, d50 = 3 cm, i = 1 in 500.

## Short answer

Since sides are protected, bed stability governs. Using Shields, stable depth = 1.16 m. Adopted section: bed width 1.6 m, depth 1.16 m, side slope 1.5H:1V.

## Answer

Given: $Q = 5\ \text{m}^3/\text{s}$, $S = 0.002000$ (1 in 500), particle size $d = 30$ mm. The sides are well protected, so the angle of repose is not needed; a side slope of 1.5H:1V (33.7° with the horizontal) is assumed. Take $\gamma = 9.81$ kN/m³ and specific gravity of particles 2.65. $n = \dfrac{d^{1/6}}{21.1} = \dfrac{0.03^{1/6}}{21.1} = 0.0264$ (Strickler).

#### Critical shear stress of the bed (Shields)

$$
\tau_c = 0.047(\gamma_s - \gamma)d = 0.047\times(2.65-1)\times 9.81\times 0.03 = 22.82\ \text{N/m}^2
$$

#### Depth limited by the bed

$$
\gamma D S \le \tau_c \Rightarrow D_{bed} = \frac{\tau_c}{\gamma S} = \frac{0.02282}{9.81\times 0.002000} = 1.16\ \text{m}
$$

The sides are well protected, so only bed stability governs: $D = D_{bed}$.

#### Bed width from Manning's equation

Using $D = 1.16$ m and $Q = \frac{1}{n}AR^{2/3}S^{1/2}$, trial gives $B = 1.59$ m; adopt $B = 1.6$ m. Check: $A = 3.87$ m², $R = 0.670$ m, $V = 1.296$ m/s, $Q = 5.02$ m³/s.

**Answer:** Stable depth $D \approx 1.16$ m, bed width $B \approx 1.6$ m, side slope 1.5H:1V.

This section is deep and narrow. Because every depth up to 1.16 m is stable, a wider and shallower section (larger $B$, smaller $D$) carrying the same discharge is equally stable and is usually preferred in practice.

## Check yourself

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

1. Since the sides are well protected, what controls the stable depth?
   A. Both side and bed, with K applied
   B. Only the angle of repose
   C. Only Manning's n
   D. Only bed stability, D = tau_c/(gamma S)
   Answer: D. Protected sides do not scour, so the angle of repose is not needed. (Key point: Protected sides)

2. What stable depth results?
   A. D = 0.02282/(9.81 x 0.002) = 1.16 m
   B. D = 0.58 m
   C. D = 2.32 m
   D. D = 3.49 m
   Answer: A. tau_c = 22.82 N/m^2 for d = 30 mm; slope is 1/500 = 0.002. (Key point: Depth value)

3. How is B found?
   A. B = tau_c/gamma
   B. Using Manning's equation with D = 1.16 m by trial, B about 1.6 m
   C. B = 4.75 sqrt(Q)
   D. B = 6D
   Answer: B. Trial gives B = 1.59 m, so Q = 5.02 m^3/s. (Key point: Bed width)

## Related in Irrigation and Drainage Engineering

- [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×
- [Stable channel: Q 20, particle 4 cm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Astable-channel-q20-particles-4cm) — Irrigation and Drainage Engineering, chapter 4
- [Stable canal: Q 40, d 5 cm](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Astable-canal-q40-d5cm-phi37) — Irrigation and Drainage Engineering, chapter 4, asked 2×
- [Stable depth: Q 50, slope 1:1000](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Astable-depth-q50-d50mm-slope1000) — Irrigation and Drainage Engineering, chapter 4, asked 2×
- [Lacey and Kennedy bed width, Q 40](https://www.bctengineer.com/question.md?key=semester_6%2Firrigation_and_drainage_engineering%3Alacey-kennedy-q40-comparison) — Irrigation and Drainage Engineering, chapter 4

## Related in other subjects

- [250/500 V transformer, parameters both sides](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atf-250-500-open-hv-test) — Electrical Machines, chapter 2
- [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 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
- [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