Question

Water flows in a rectangular concrete channel and undergoes a hydraulic jump such that half of its mechanical energy gets dissipated. If the channel carries 10cumecs water energy at a depth of 0.6 m and the width of channel is 5 m, the Froude number after the jump is.

• A. 0.2

Answer 1

The correct option is A 0.2
Given: B=5 m, Q=10cumecs,
$y_1=0.6m$

$E_1=y_1+\frac{Q^2}{2g{B}^2{y}_1^2}$

$=0.6+\frac{(10{)}^2}{2\times 9.81\times 25(0.6{)}^2}=1.166m$

$E_L=0.5E_1$

$\frac{(y_2-y_1{)}^3}{4y_1{y}_2}=0.5\times 1.166$

$\frac{(y_2-0.6{)}^3}{4\times 0.6y_2}=0.583$

$y_2^3-0.216-1.8y_2^3+1.08y_2=1.4y_2$

$y_2^3-1.8y_2^2-0.32y_2-0.216=0$

$y_2=2m,-0.106m,-0.106m$

$\Rightarrow y_2=2m$

$F_2=\frac{V}{\sqrt{g{y}_2}}=\frac{\frac{10}{5}\times 2}{\sqrt{9.81\times 2}}=0.225$