Question

For a smooth hump in a sub-critical flow to function as a broad crested weir, the height $\Delta Z$ of the hump above the bed must satisfy which one of the following?
( Where, $E_1$=Specific head upstream of the hump.
$E_c$= Specific head at the critical depth $y_c$ ,
Neglect friction effect )

• A. $\Delta Z\ge (E_1-E_c)$
  
• B. $\Delta Z\ge (E_1-y_c)$
• C. $\Delta Z\le (E_1-y_c)$
• D. $\Delta Z\le (E_1-E_c)$

Answer 1

The correct option is D $\Delta Z\le (E_1-E_c)$

(d) If the flow is subcritical, then after the introduction of hump the specific energy will decrease by $\Delta Z$
(height of hump).

$E_c\le E_1-\Delta Z$

$\Rightarrow \Delta Z\le E_1-E_c$