---
title: "Uniform flow in rectangular channel (Chezy)"
subject: "Hydro Power"
chapter: 1
key: "semester_6/hydro_power:rectangular-channel-chezy-flow"
source: https://www.bctengineer.com/q/semester_6/hydro_power/rectangular-channel-chezy-flow
site: BCT Engineering
---

# Uniform flow in rectangular channel (Chezy)

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

- Asked in: 2075 Baisakh, 8 marks
- Video: [Uniform Flow in Open Channels | Chezy’s & Manning’s Equation | Most Efficient Channel Section](https://www.youtube.com/watch?v=2QP3FEBdFjo) — learn with Patel 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/hydro_power/rectangular-channel-chezy-flow
- Whole chapter: https://www.bctengineer.com/md/semester_6/hydro_power/chapter-1

## Question

Find the rate of flow for a rectangular channel 7.5 m wide for uniform flow at a depth of 2.25 m. The channel is having bed slope as 1 in 1000. Take Chezy's constant C = 55.

## Short answer

Using Chezy's formula: A=16.875 m², P=12 m, R=1.406 m. Velocity V=55√(1.406×1/1000)=2.063 m/s, discharge Q=34.8 m³/s.

## Answer

Uniform flow in an open channel is given by Chezy's formula $Q = AC\sqrt{RS}$.

#### Section properties
$$
\begin{aligned}
A &= by = 7.5 \times 2.25 = 16.875\ \text{m}^2 \\
P &= b + 2y = 7.5 + 2 \times 2.25 = 12.0\ \text{m} \\
R &= \frac{A}{P} = \frac{16.875}{12} = 1.406\ \text{m}
\end{aligned}
$$

#### Velocity and discharge
$$
\begin{aligned}
V &= C\sqrt{RS} = 55\sqrt{1.406 \times \frac{1}{1000}} = 55 \times 0.0375 = 2.063\ \text{m/s} \\
Q &= AV = 16.875 \times 2.063 = 34.80\ \text{m}^3/\text{s}
\end{aligned}
$$

**Answer:** Rate of flow $Q \approx 34.8$ m³/s (velocity ≈ 2.06 m/s).

## Check yourself

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

1. Which formula gives velocity here?
   A. V = C sqrt(RS)
   B. V = C R S
   C. V = sqrt(2gy)
   D. V = (1/n) R^(2/3) S^(1/2)
   Answer: A. Chezy: V = C sqrt(RS), then Q = AV. (Key point: Formula)

2. For b = 7.5 m and y = 2.25 m, the wetted perimeter is:
   A. 9.75 m
   B. 12.0 m
   C. 16.875 m
   D. 15.0 m
   Answer: B. P = b + 2y = 7.5 + 4.5 = 12.0 m (the free surface is not wetted). (Key point: Perimeter)

3. The hydraulic radius is:
   A. 2.25 m
   B. 1.406 m
   C. 0.71 m
   D. 7.5 m
   Answer: B. R = A/P = 16.875/12 = 1.406 m. (Key point: Hydraulic radius)

4. The discharge is approximately:
   A. 34.8 m^3/s
   B. 2.06 m^3/s
   C. 16.9 m^3/s
   D. 69.6 m^3/s
   Answer: A. V = 55 sqrt(1.406/1000) = 2.063 m/s and Q = 16.875 x 2.063 = 34.8 m^3/s. (Key point: Discharge)

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