Open Channel Flow MCQ with answer and solution

Concept

Saint Venant Equations

Formula

Continuity equation: ∂A/∂t + ∂Q/∂x = 0; Momentum equation: ∂v/∂t + v(∂v/∂x) + g(∂y/∂x) = g(S0 - Sf)

Step-by-step solution

1. Identify the physical principles governing 1D unsteady open channel flow: mass conservation and momentum conservation. 2. Associate mass conservation with the continuity equation and momentum conservation with the momentum equation. 3. Conclude that the Saint Venant equations represent both the continuity and momentum equations (Option A).

Explanation

The Saint Venant equations represent the continuity equation (conservation of mass) and the momentum equation (conservation of momentum) to describe unsteady flow in open channels.

Shortcut

Remember "Saint = C & M" (Continuity and Momentum). Saint Venant governs unsteady flow by balancing mass (Continuity) and motion (Momentum).

Common mistake

Many students mistakenly choose Option D (Momentum and energy equations) because they confuse the Saint Venant equations with general open channel hydraulics or Bernoulli-based equations, assuming energy conservation is explicitly part of the system rather than continuity (mass conservation) and momentum conservation.