Question

A 1 m wide rectangular channel has a bed slope of 0.0016 and Manning's roughness coefficient is 0.04. Uniform flow takes place in the channel at a flow depth of 0.5 m. At a particular section, gradually varied flow (GVF) is observed and the flow depth is measured as 0.6 m. The GVF profile at that section is classified as

• A. $M_2$
• B. $S_1$
• C. $M_1$
• D. $S_2$

Answer 1

The correct option is C $M_1$

$Q=\frac{1}{n}\times A\times R^{2/3}\times S^{1/2}$

$A=1\times 0.5=0.5m^2$

$P=1+(0.5\times 2)=2m$

$Q=\frac{1}{0.04}\times 0.5\times {\left(\frac{0.5}{2}\right)}^{2/3}\times (0.0016{)}^{1/2}$

$=0.1984m^3/s$

$q=\frac{Q}{1}=0.1984m^3/s/m$

For rectangular channel

$y_c={\left(\frac{q^2}{g}\right)}^{1/3}={\left(\frac{{0.1984}^2}{9.81}\right)}^{1/3}=0.159m$

Since, $y_n>y_{c}ThusitisMildSlope$