Question

A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete (Manning's n = 0.012). The hydraulic radius (in m) for depth of flow of 3.0 m is

• A. 3.0
• B. 3.5
• C. 20.0
• D. 2.1

Answer 1

The correct option is D 2.1


$\because A=(B+ny)y=(10+\frac{4}{3}\times 3)\times 3$
$=(10+4)3=42m^2$
$P=B+2y\sqrt{n^2+1}$
$=10+6\sqrt{{\left(4/3\right)}^2+1}$
$=10+6\times \frac{5}{3}=20m$
$\therefore R=\frac{A}{P}=\frac{42}{20}=2.1$