Open Channel Flow MCQ with answer and solution

Concept

In a circular channel, the maximum discharge does not occur when the pipe is fully full, but rather at a specific depth slightly less than the diameter due to friction and hydraulic radius properties.

Formula

Q = A × V Q_max at d = 0.81D (approx)

Step-by-step solution

1. Understand what is asked: We need to find the depth of water in a circular channel where the discharge is maximum. 2. In fluid mechanics and open channel flow, as water depth increases in a circular pipe, both area and hydraulic radius change. 3. By differentiating the discharge equation with respect to depth and equating to zero, we find that maximum discharge occurs at approximately 0.81 times the diameter of the circular channel. Answer: (C) 0.81

Explanation

Maximum discharge in a circular channel occurs at a depth of 0.81D because of the optimal balance between flow area and wetted perimeter. Maximum velocity occurs at a slightly lower depth, around 0.5D.

Why the other options are wrong

A: 0.34 is not a standard maximum flow point. B: 0.67 is incorrect for maximum discharge. D: 0.95 is the depth for maximum hydraulic mean depth (velocity), not discharge.

Shortcut

Remember: Maximum velocity is at 0.5D, maximum discharge is at 0.81D, and maximum hydraulic mean depth is at 0.95D.

Common mistake

Students often think maximum discharge occurs when the pipe is 100% full (1.0D), forgetting that wetted perimeter increases sharply at the top without adding much flow area.