Question

For a given discharge, the critical flow depth in an open channel depends on

• A. Channel geometry only
• B. Channel geometry and bed slope
• C. Channel geometry, bed slope and roughness
• D. Channel geometry, bed slope, roughness and Reynolds number

Hint:

Remember: \[ \boxed{\text{Critical Depth}} \] depends on \[ \boxed{\text{Discharge + Channel Geometry}} \] whereas \[ \boxed{\text{Normal Depth}} \] depends on discharge, bed slope, and roughness.

Answer 1

The Correct Option is A

Concept: Critical flow occurs when the specific energy is minimum for a given discharge. The condition for critical flow is \[ \boxed{Fr=1} \] where \(Fr\) is the Froude number. The critical depth depends only on the discharge and the geometry of the channel section. It is independent of the bed slope, roughness, and Reynolds number.

Step 1: Understand critical depth. For a given discharge, \[ Q=\text{Constant}, \] critical depth is determined solely by the shape and dimensions of the channel.

Step 2: Identify the influencing factors. Neither bed slope nor channel roughness affects the critical depth. Hence, \[ \boxed{\text{Critical depth depends only on the channel geometry}.} \] Therefore, the correct option is \[ \boxed{(A)\;\text{Channel geometry only}.} \]