Question

Water is flowing in a horizontal, frictionless, rectangular channel. A smooth hump is built on the channel floor at a section and its height is gradually increased to reach choked condition in the channel. The depth of water at this section is \(y_2\) and that at its upstream section is \(y_1\). The correct statement(s) for the choked and unchoked conditions in the channel is/are

• A. In choked condition, \(y_1\) decreases if the flow is supercritical and increases if the flow is subcritical.
• B. In choked condition, \(y_2\) is equal to the critical depth if the flow is supercritical or subcritical.
• C. In unchoked condition, \(y_1\) remains unaffected when the flow is supercritical or subcritical.
• D. In choked condition, \(y_1\) increases if the flow is supercritical and decreases if the flow is subcritical.

Hint:

In open channel flow, the critical depth is the depth at which the flow transitions from subcritical to supercritical, and the flow behavior is highly sensitive to the channel conditions.

Answer 1

The Correct Option is A, B, C

- (A) is correct as the depth \(y_1\) behaves differently for supercritical and subcritical flows in choked conditions. In supercritical flow, the depth decreases, while in subcritical flow, the depth increases.
- (B) is correct because, in choked conditions, the water depth at the section \(y_2\) reaches the critical depth, as it is the state where the flow becomes critical.
- (C) is correct because in unchoked conditions, the upstream depth \(y_1\) remains unaffected by whether the flow is supercritical or subcritical.
- (D) is incorrect because \(y_1\) behaves oppositely to what is stated in supercritical and subcritical flow conditions.
Thus, the correct answer is:
\[ \boxed{\text{(A), (B), (C)}}. \]