Question

A hydraulic jump is formed in a 2 m wide rectangular channel which is horizontal and frictionless. The post-jump depth and velocity are 0.8 m and 1 m/s, respectively. The pre-jump velocity is m/s. (use $g=10m/s^2$)

• A. 4.83 m/s
• B. 0.83 m/s
• C. 2.83 m/s
• D. 3.58 m/s

Answer 1

The correct option is A 4.83 m/s

$y_2=0.8m$
$v_2=1m/s$
$F_{r_2}=\frac{v_2}{\sqrt{gD}}=\frac{1}{\sqrt{10\times \frac{0.8\times 2}{2}}}$
$F_{r_2}=0.3535$
$y_1=\frac{y_2}{2}(-1+\sqrt{1+8F_{r_2}^2})$
$\frac{0.8}{2}(-1+\sqrt{1+8\times {0.3535}^2})$
= 0.165643
$\Rightarrow v_1{y}_1=v_2{y}_2$
$\Rightarrow v_1=\frac{1\times 0.8}{0.165643}=4.83m/s$