In open channel control design, how can critical depth be produced for a given discharge in a prismatic channel?

Introduction / Context:Critical depth controls are used for flow measurement and to stabilize flow regimes. Creating critical depth involves modifying specific energy conditions at a control section.

Given Data / Assumptions:

• Steady, prismatic channel with given discharge.
• Objective is to induce critical state (Froude number = 1) at a section.

Concept / Approach:For a fixed discharge, critical depth corresponds to minimum specific energy. A control structure that increases specific energy demand relative to depth can force the flow to pass through the critical state.

Step-by-Step Solution:Raising the bed (hump) effectively reduces available specific energy at a section, pushing the flow toward critical depth.Decreasing the width (contraction) increases velocity for the same discharge, increasing velocity head and promoting a critical state.Lowering the bed or increasing width generally moves conditions away from critical for the same discharge.Thus, both a hump and a contraction can produce critical depth.

Verification / Alternative check:Specific energy diagrams show a control shifting the operating point onto the critical curve for the given discharge.

Why Other Options Are Wrong:

• Lowering the bed or increasing width typically increases depth for the same energy and does not enforce criticality.

Common Pitfalls:

• Ignoring energy losses; real controls introduce minor head losses but the critical condition remains a useful design target.

Final Answer:Both (a) and (c)