Open-Channel Flow – Critical depth criterion Critical depth occurs in an open channel under which of the following conditions?

Introduction / Context:
Critical flow separates subcritical (tranquil) from supercritical (rapid) regimes. It is fundamental in flow measurement, control structures, and analysis of hydraulic jumps. Several equivalent definitions exist, but the most common exam-standard statement uses the specific energy criterion.

Given Data / Assumptions:

• Steady, one-dimensional flow in a prismatic channel.
• Specific energy E = y + V^2/(2g) for a given discharge.
• Froude number Fr = V/√(g D_h) equals 1 at critical (D_h is hydraulic depth).

Concept / Approach:

For a fixed specific energy E, the discharge Q achieves a maximum at the critical state; equivalently, for a fixed Q, the specific energy is a minimum at critical. The E–Q relationship is such that the curve has a single peak at critical conditions, and the two possible depths for a given E (subcritical and supercritical) coalesce there.

Step-by-Step Solution:

Verification / Alternative check:

Momentum (specific force) formulation gives an equivalent criterion: for given discharge, the specific force is minimum at critical. These parallel statements confirm the central role of the critical state.

Why Other Options Are Wrong:

(b) reverses the correct extremum (E is minimum, not maximum). (c) states the opposite of (a). (d) is less commonly used and, while momentum-based maxima/minima can be formulated, the standard single-correct choice in such questions is (a).

Common Pitfalls:

Confusing “maximum E” with “minimum E,” and mixing energy and momentum criteria without keeping discharge or E constant.

Final Answer:

For a given specific energy, the discharge is maximum