Question

A 4 m wide rectangular channel carries water at Froude number of flow $\sqrt{10}$ at a depth of 1 m. The water experiences a hydraulic jump, the Froude number downstream of the jump is____

• A. 0.395

Answer 1

The correct option is A 0.395
Given,
$y_1=1m,F_1=\sqrt{10},B=4m$

$F_1=\frac{V_1}{\sqrt{g{y}_1}}$

$\sqrt{10}=\frac{V_1}{\sqrt{9.81\times 1}}\Rightarrow V_1=9.9m/sec$

Downstream depth,

$y_2=\frac{y_1}{2}[\sqrt{1+8F_1^2}-1]$

$=\frac{1}{2}[\sqrt{1+80}-1]=4m$

Now,
$q=V_1{Y}_1=V_2{Y}_2$

$V_2=\frac{9.9\times 1}{4}=2.475m/sec$

$\therefore F_2=\frac{V_2}{\sqrt{g{y}_2}}=\frac{2.475}{\sqrt{9.81\times 4}}=0.395$