---
title: "Chezy's and Manning's coefficient for Seti River"
subject: "Hydraulics"
chapter: 6
key: "semester_4/hydraulics:seti-river-chezy-manning-coefficient"
source: https://www.bctengineer.com/q/semester_4/hydraulics/seti-river-chezy-manning-coefficient
site: BCT Engineering
---

# Chezy's and Manning's coefficient for Seti River

Hydraulics · Chapter 6: Uniform flow in open channel

- Asked in: 2076 Bhadra, 2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/hydraulics/seti-river-chezy-manning-coefficient
- Whole chapter: https://www.bctengineer.com/md/semester_4/hydraulics/chapter-6

## Question

The longitudinal bed slope of Seti River is 10 cm to a kilometer with hydraulic mean depth of 2.5 m. Find Chezy's coefficient and Manning's rugosity coefficient, if the velocity at the peak flood is measured to be 2.4 m/s.

## Short answer

Using bed slope 1×10⁻⁴, hydraulic radius 2.5 m and velocity 2.4 m/s, Chezy's C = V/√(RS) = 151.8 m¹/²/s. Manning's n = R¹/⁶/C = 0.0077 s/m¹/³.

## Answer

#### Given data
Bed slope $S=\dfrac{10\ \text{cm}}{1\ \text{km}}=\dfrac{0.1}{1000}=1\times10^{-4}$, hydraulic mean depth $R=2.5$ m, $V=2.4$ m/s.

#### Chezy's coefficient
$$
V=C\sqrt{RS}\;\Rightarrow\;C=\frac{V}{\sqrt{RS}}=\frac{2.4}{\sqrt{2.5\times10^{-4}}}=\frac{2.4}{0.015811}=151.79\ \text{m}^{1/2}/\text{s}
$$

#### Manning's coefficient
$$
C=\frac{R^{1/6}}{n}\;\Rightarrow\;n=\frac{R^{1/6}}{C}=\frac{2.5^{1/6}}{151.79}=\frac{1.1650}{151.79}=0.00768
$$
(Check with Manning: $V=\dfrac1nR^{2/3}S^{1/2}=\dfrac{1}{0.00768}\times1.842\times0.01=2.40$ m/s.)

**Answer: $C=151.8$ m$^{1/2}$/s and $n=0.0077$ s/m$^{1/3}$.** The value of $n$ is very low for a natural river; it follows directly from the data as given.

## Check yourself

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

1. What is the bed slope of 10 cm per km?
   A. 1 x 10^-4
   B. 1 x 10^-3
   C. 1 x 10^-2
   D. 1 x 10^-5
   Answer: A. 0.1 m / 1000 m = 1 x 10^-4. (Key point: Slope)

2. How is Chezy's C found and what is its value?
   A. C = V sqrt(RS) = 0.038
   B. C = V/sqrt(RS) = 151.8
   C. C = V R S = 0.06
   D. C = sqrt(V/RS) = 98
   Answer: B. V = C sqrt(RS), so C = 2.4/0.01581 = 151.8. (Key point: Chezy C)

3. Which relation gives Manning's n from C?
   A. n = C R^(1/6)
   B. n = C/R^(1/6)
   C. n = R^(1/6)/C
   D. n = R^(2/3)/C
   Answer: C. C = R^(1/6)/n, so n = 1.165/151.8 = 0.0077. (Key point: Manning n)

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