Question

A 4 m wide rectangular channel carries water at Froude number $\sqrt{10}$ at a depth of 1 m. If the water undergoes hydraulic jump, the Froude number downstream of the jump will be?

• A. 0.75 m
• B. 0.39 m
• C. 0.61 m
• D. 1.2 m

Answer 1

The correct option is B 0.39 m

Given, $F_1=\sqrt{10},y_1=1m,B=4m$

$F_1=\frac{V}{\sqrt{g{y}_1}}\Rightarrow V=\sqrt{10}\times \sqrt{9.81\times 1}=9.9m/sec$

$\therefore Q=\left(B{y}_1\right)\times V$

$=(4\times 1)\times 9.9=39.6m^3/sec$

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

$=\frac{1}{2}[\sqrt{1+8\times 10}-1]=4m$

$F_2=\frac{V_2}{\sqrt{g{y}_2}}=\frac{39.6}{4\times 4\sqrt{9.81\times 4}}=0.395$