Section 4: Soil and Water Conservation Engineering
Fluid Mechanics
Subtopic: Flow in open channels
Question Statement:
In a wide rectangular channel carrying a discharge per unit width of $q$, the critical depth $y_c$ and minimum specific energy $E_{min}$ are related by:
Options:
(A) $E_{min} = 1.5 y_c$
(B) $E_{min} = 2.0 y_c$
(C) $E_{min} = 1.25 y_c$
(D) $E_{min} = 2.5 y_c$
Answer Key:
A
Step-by-Step Solution & Explanation
For a rectangular channel, specific energy is given by:
$E = y + \frac{q^2}{2 g y^2}$
At critical depth, $q^2 / g = y_c^3$, which gives $\frac{q^2}{2 g y_c^2} = \frac{y_c}{2}$.
Therefore:
$E_{min} = y_c + \frac{y_c}{2} = 1.5 y_c$