Specific Energy in Open Channel Flow MCQ with answer and solution

Concept

Critical flow occurs when the Froude number is equal to unity, representing a state of minimum specific energy for a constant discharge.

Formula

E = y + Q² / (2gA²); dE/dy = 0 for minimum energy.

Step-by-step solution

1. Define Specific Energy (E) as the energy per unit weight of water at any section of a channel measured with respect to the channel bottom. 2. Write the equation: E = y + V²/(2g). 3. To find the condition for minimum specific energy for a constant discharge (Q), differentiate E with respect to depth (y) and set it to zero (dE/dy = 0). 4. This mathematical condition yields the critical depth (yc), at which the flow is termed 'critical'.

Explanation

Critical flow is defined as the flow condition where the specific energy is minimum for a given discharge. Alternatively, it is the condition where the discharge is maximum for a given specific energy.

Why the other options are wrong

A: Specific energy is minimum, not maximum, at critical depth. C: Discharge is maximum for a *given* specific energy, but the standard definition of critical flow state is based on minimum energy for a given discharge. D: Velocity is never zero in a flowing channel; at critical flow, velocity equals √(g × hydraulic depth).

Shortcut

Remember: 'Minimum Energy' or 'Maximum Discharge' = Critical Flow.

Common mistake

Confusing maximum energy with minimum energy. In open channel flow, we always look for the minimum energy point on the E-y curve.