Question

For a wide rectangular channel using Manning's formula, the differential equation of gradually varied flow (with the usual notations) is given by

• A. $\frac{dy}{dx}=S_0\frac{[1-{\left(\frac{y_0}{y}\right)}^3]}{[1-{\left(\frac{y_c}{y}\right)}^3]}$
• B. $\frac{dy}{dx}=S_0\frac{[1-{\left(\frac{y_c}{y}\right)}^{10/3}]}{[1-{\left(\frac{y_0}{y}\right)}^3]}$
• C. $\frac{dy}{dx}=S_0\frac{[1-{\left(\frac{y_c}{y}\right)}^3]}{[1-{\left(\frac{y_0}{y}\right)}^3]}$
• D. $\frac{dy}{dx}=S_0\frac{[1-{\left(\frac{y_0}{y}\right)}^{10/3}]}{[1-{\left(\frac{y_c}{y}\right)}^3]}$

Answer 1

The correct option is D

$\frac{dy}{dx}=S_0\frac{[1-{\left(\frac{y_0}{y}\right)}^{10/3}]}{[1-{\left(\frac{y_c}{y}\right)}^3]}$

$\frac{dy}{dx}=S_0\frac{1-{\left(y_0/y\right)}^N}{1-{\left(y_c/y\right)}^M}$

For Chezy's formula, N=3 M=3
For Manning's formula, N=10/3 M=3

$Nisrelatedtoconveyance\left(\frac{1}{n}{S}^{1/2}{R}^{2/3}\right)$