Question

A rectangular channel 6.0 m wide carries a discharge of 16.0$m^3/s$ under uniform flow condition with normal depth of 1.60 m. Manning's 'n' is 0.015.

The longitudinal slope of the channel is

• A. 0.000585
• B. 0.000485
• C. 0.000385
• D. 0.000285

Answer 1

The correct option is A 0.000585

The velocity per Manning's equations is given by

$V=\frac{1}{n}{R}^{2/3}{S}^{1/2}$

Here, $Q=16m^3/s,n=0.015,B=6.0m$

$A=6.0\times 1.60=9.6m^2$

$R=\frac{A}{P}=\frac{9.6}{6.0+(1.6\times 2)}=1.04m$

But Q = AV

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

$\Rightarrow 16=9.6\times \frac{1}{0.015}\times (1.04{)}^{2/3}\times S^{1/2}$

$\Rightarrow S=0.00059$