The relation between Manning' 'n' and Chezy's 'C' is given by

Where R = hydraulic mean depth

This question was previously asked in
UKPSC JE Civil 2013 Official Paper II
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  1. \(C = \frac{{{R^{1/6}}}}{n}\)
  2. \(C = \frac{{{R^{2/3}}}}{n}\)
  3. \(C = \frac{{{R^{1/3}}}}{n}\)
  4. \(C = \frac{{{R^{1/4}}}}{n}\)

Answer (Detailed Solution Below)

Option 1 : \(C = \frac{{{R^{1/6}}}}{n}\)
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Detailed Solution

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Explanation:

Manning's Formula:

\(V = \frac{1}{n} \times {\left( R \right)^{\frac{2}{3}}}{\left( S \right)^{\frac{1}{2}}}\)...... (1)

Chezy formula:

V = C \(\sqrt{RS}\)........ (2)

where

n = Manning’s Coefficient

R = Hydraulic radius = (Wetted Area/ Wetted Perimeter)

S = Bed Slope

C = Chezy's Coefficient

From Equations 1 and 2

\(C = \frac{{{R^{1/6}}}}{n}\)

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