---
title: "Best hydraulic rectangular canal design"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:best-rectangular-canal-design"
source: https://www.bctengineer.com/q/semester_6/hydro_power/best-rectangular-canal-design
site: BCT Engineering
---

# Best hydraulic rectangular canal design

Hydro Power · Chapter 1: Introduction to Basic Fluid Mechanics and Hydraulics

- Asked in: 2081 Asoj, 5 marks
- Video: [Hydraulically Efficient Rectangular Channel Section](https://www.youtube.com/watch?v=hSnQR1dZoYM) — WATERCORE
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/best-rectangular-canal-design
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Design the best hydraulic rectangular cross-section for a canal conveying 15 m³/s discharge with Manning's n = 0.02 and a bed slope of 0.001.

## Short answer

For the best hydraulic rectangular section, width b = 2y. Solving Manning's equation with Q=15 m³/s, n=0.02, S=0.001 gives depth 2.13 m, width 4.26 m, and velocity 1.65 m/s.

## Answer

For the best hydraulic rectangular section, width is twice the depth: $b = 2y$, so $A = 2y^2$ and $R = y/2$.

#### Manning's equation
$$
\begin{aligned}
Q &= \frac{1}{n}AR^{2/3}S^{1/2} \\
15 &= \frac{1}{0.02}(2y^2)\left(\frac{y}{2}\right)^{2/3}(0.001)^{1/2} \\
15 &= 50 \times 2 \times 0.63 \times 0.03162\, y^{8/3} = 1.992\,y^{8/3} \\
y^{8/3} &= 7.529 \;\Rightarrow\; y = 7.529^{3/8} = 2.132\ \text{m}
\end{aligned}
$$

#### Section
$$
\begin{aligned}
b &= 2 \times 2.132 = 4.264\ \text{m} \\
A &= 2 \times 2.132^2 = 9.091\ \text{m}^2, \quad R = 1.066\ \text{m} \\
V &= 15/9.091 = 1.65\ \text{m/s}
\end{aligned}
$$
Check: $50 \times 9.091 \times 1.066^{2/3} \times 0.03162 = 15.0$ m³/s.

```text
   |<---- b = 4.26 m ---->|
   |~~~~~~~~~~~~~~~~~~~~~~|
   |                      |  y = 2.13 m
   |______________________|
```

**Answer:** Width ≈ 4.26 m, depth ≈ 2.13 m (plus freeboard), velocity ≈ 1.65 m/s.

## Check yourself

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

1. For the best hydraulic rectangular section, which are the area and R?
   A. A = 2y^2, R = y/2
   B. A = y^2, R = y
   C. A = 2y^2, R = y
   D. A = 4y^2, R = y/4
   Answer: A. With b = 2y, A = 2y^2 and R = y/2. (Key point: Best rectangle)

2. Substituting into Manning's equation leaves the unknown as:
   A. y^2
   B. y^(8/3)
   C. y^(1/3)
   D. y^5
   Answer: B. A R^(2/3) proportional to y^2 x y^(2/3) = y^(8/3); 15 = 1.992 y^(8/3). (Key point: Manning reduction)

3. The depth of flow is about:
   A. 1.07 m
   B. 2.13 m
   C. 4.26 m
   D. 7.53 m
   Answer: B. y = 7.529^(3/8) = 2.132 m. (Key point: Depth)

4. The corresponding width and velocity are:
   A. b = 2.13 m, V = 3.3 m/s
   B. b = 4.26 m, V = 1.65 m/s
   C. b = 4.26 m, V = 0.65 m/s
   D. b = 8.5 m, V = 1.65 m/s
   Answer: B. b = 2y = 4.264 m, A = 9.091 m^2, V = 15/9.091 = 1.65 m/s. (Key point: Width and velocity)

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