Gradually Varied Flow MCQ with answer and solution

Concept

Gradually Varied Flow Profiles

Formula

Yes, the dynamic equation for gradually varied flow is given by: dy/dx = (S0 - Sf) / (1 - Fr²) Where: - dy/dx = slope of the water surface relative to the channel bed - S0 = channel bed slope - Sf = friction slope - Fr = Froude number

Step-by-step solution

1. Identify the bed slope (S0) and friction slope (Sf) of the channel. 2. Determine the Froude number (Fr) to identify whether the flow is subcritical (Fr \< 1) or supercritical (Fr \> 1). 3. Evaluate the sign of dy/dx = (S0 - Sf) / (1 - Fr²) to determine if the water surface profile rises or falls along the flow direction.

Explanation

In gradually varied flow, the shape of the water surface profile depends on the bed slope of the channel (mild, steep, critical, horizontal, or adverse), the actual depth of water relative to normal and critical depths, and the type of flow regime (subcritical or supercritical). Together, these factors define the specific flow profile (such as M1, M2, S1, etc.).

Shortcut

Remember the acronym S-D-T(Slope, Depth, Type): - Slope of the channel (mild, steep, critical, etc.) - Depth of flow (actual depth relative to normal and critical depths) - Type of flow regime (subcritical or supercritical)

Common mistake

Many students mistakenly choose Option A (The Froude number only) because the Froude number plays a critical role in determining subcritical vs. supercritical flow, overlooking that the overall surface profile classification also requires knowing the channel bed slope and actual flow depth relative to normal/critical depths.