Question

There is subcritical flow in a rectangular channel as shown.

In this channel at section B, a hump is provided which has a height less than the critical height of the hump. Then [Neglect all the losses]

• A. $y<(y_1+\Delta Z)$
• B. $y>(y_1+\Delta Z)$
• C. Data insufficient
• D. $y=y+1\Delta Z$

Answer 1

The correct option is B $y>(y_1+\Delta Z)$

Applying energy equation
$E_A=E_B$

$\Rightarrow y+\frac{q^2}{2g{y}^2}=y_1+\frac{q^2}{2g{y}_1^2}+\Delta Z$

$\Rightarrow (y-y_1)+\frac{q^2}{2g}\left(\frac{y_1^2-y^2}{y_1^2{y}^2}\right)=\Delta Z$

$\Rightarrow y=y_1+\Delta Z-\frac{q^2}{2g}\left(\frac{y_1^2-y^2}{y_1^2{y}^2}\right)$

$\Rightarrow y>y_1+\Delta Z(\because y_1^2-y^{2}isnegative)$