Question

A rectangular open channel of width 5.0 m is carrying a discharge of $100m^3/s$. The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is

• A. 5
• B. 4
• C. 16
• D. 20

Answer 1

The correct option is B 4

$\because FroudeNumber,$
$F=\frac{V}{\sqrt{gy}}$

$\Rightarrow 0.8=\frac{V}{\sqrt{9.81y}}$ ...(i)

$\because Q=AV$

$\Rightarrow 100=\left(5y\right)V$

$\Rightarrow V=\frac{100}{5y}=\frac{20}{y}$

$\therefore Fromeq.\left(i\right)$

$0.8=\frac{20}{\sqrt{9.81}.(y{)}^{3/2}}$

$\Rightarrow y^{3/2}=\frac{20}{0.8\sqrt{9.81}}$

$\therefore y=3.99\simeq 4m$