Specific Energy in Open Channel Flow MCQ with answer and solution

Concept

Alternate Depths and Specific Energy

Formula

E = y + V² / (2g)

Step-by-step solution

1. Identify the depth of flow (y) and the flow velocity (V). 2. Calculate the velocity head using the formula V² / (2g), where g is acceleration due to gravity. 3. Add the depth of flow to the velocity head: E = y + V² / (2g). 4. Note that for any specific energy E greater than E\_min, two alternate depths exist (one subcritical and one supercritical).

Explanation

For any value of specific energy greater than the minimum specific energy, two different depths of flow are possible (known as alternate depths). One depth is larger with a low velocity, corresponding to subcritical flow, while the other depth is smaller with a high velocity, corresponding to supercritical flow. Therefore, the flow can be either subcritical or supercritical.

Shortcut

Remember "E > Emin = 2 Depths (Sub & Super)". Above minimum specific energy, the E-y curve splits into two branches: Subcritical (above critical depth) and Supercritical (below critical depth).

Common mistake

A common mistake is selecting either "Only subcritical" or "Only supercritical" by assuming only one depth can exist for a given specific energy, rather than recognizing that two alternate depths exist (one subcritical and one supercritical) for any energy level above the minimum specific energy.