The relationship between Manning's coefficient and Chezy's coefficient is given by

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BPSC AE Paper 6 (Civil) 14 Oct 2022 Official Paper
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  1. C = \(\frac{1}{n} R^{1 / 3}\)
  2. C = \(\frac{1}{n} R^{1 / 4}\)
  3. C = \(\frac{1}{n} R^{1 / 6}\)
  4. C = \(\frac{1}{n} R^{2 / 3}\)

Answer (Detailed Solution Below)

Option 3 : C = \(\frac{1}{n} R^{1 / 6}\)
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Detailed Solution

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Calculation:

Chezy's Formula:

\(V = C\sqrt{RS}\)  ............................ (i)

Manning's Formula:

\(V = \frac{1}{n}R^{2/3}S^{1/2}\)  .......................... (ii)

where C = Chezy's Constant

R = Hydraulic Radius

S = Hydraulic Gradient Line

 n = Manning's Roughness Coefficient

From equations (i) and (ii)

\(V = C\sqrt{RS} = \frac{1}{n}R^{2/3}S^{1/2}\)

\(C(R^{1/2}) = \frac{1}{n}(R^{2/3})\)

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

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