Question

If $F_{1}and{F}_2$ are the Froude numbers of flow before and after the hydraulic jump occurring in a rectangular channel, then

• A. $F_2^2=\frac{F_1^2}{{(-1+\sqrt{1+8F_1^2})}^3}$
• B. $F_2^2=\frac{F_1^2}{{(-0.5+\sqrt{1+8F_1^2})}^3}$
• C. $F_2^2=\frac{8F_1^2}{{(-1+\sqrt{1+8F_1^2})}^3}$
• D. $F_2^2=\frac{8F_1^2}{{(-0.5+\sqrt{1+F_1^2})}^3}$

Answer 1

The correct option is C

$F_2^2=\frac{8F_1^2}{{(-1+\sqrt{1+8F_1^2})}^3}$

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

$\frac{y_1}{y_2}=\frac{(-1+\sqrt{1+8F_2^2})}{2}$

Equating the equation (i) with inverse of equation (ii) we get

$F_2^2=\frac{8F_1^2}{{(-1+\sqrt{1+8F_1^2})}^3}$

$F_1^2=\frac{8F_2^2}{{(-1+\sqrt{1+8F_2^2})}^3}$