Section 4: Soil and Water Conservation Engineering
Open Channel Flow
Subtopic: Open Channel Flow
Question Statement:
In Gradually Varied Flow (GVF), the governing differential equation for water surface profile is:
Options:
(A) $\frac{dy}{dx} = \frac{S_0 - S_f}{1 - Fr^2}$
(B) $\frac{dy}{dx} = \frac{S_f - S_0}{1 + Fr^2}$
(C) $\frac{dy}{dx} = S_0 - S_f$
(D) $\frac{dy}{dx} = 1 - Fr^2$
Answer Key:
A
Step-by-Step Solution & Explanation
From energy equation differentiation, $\frac{dy}{dx} = \frac{S_0 - S_f}{1 - Fr^2}$, where $S_0$ is bed slope, $S_f$ is friction slope, and $Fr$ is Froude number.