Critical depth definition — specific energy minimum in open channel flow The depth of water at which the specific energy is minimum is called the critical depth. Do you agree?

Introduction / Context:Specific energy E for open channel flow (per unit weight) is defined as E = y + v^2/(2g), where y is flow depth and v is mean velocity. The depth that minimizes E for a given discharge is the critical depth, a cornerstone concept in gradually varied flow and control transitions.

Given Data / Assumptions:

• Steady, prismatic channel with discharge per unit width q (for simplicity).
• Negligible energy losses across the control section.
• Hydrostatic pressure distribution.

Concept / Approach:For given q, E(y) = y + q^2/(2 g y^2) (rectangular channel). The minimum of E occurs where dE/dy = 0, yielding the critical condition. The associated Froude number Fr = v/√(g y) equals 1 at critical depth. The definition (depth at minimum E) is general and underpins control sections like weirs and flumes.

Step-by-Step Solution:

Verification / Alternative check:Plotting E vs. y shows a distinct minimum at y_c. Alternately, using Fr = 1 criteria confirms the same critical condition.

Why Other Options Are Wrong:

• Limiting to rectangular or wide channels is unnecessary; the definition of critical depth via minimum specific energy extends with appropriate geometric relations.
• Fr = 0 never occurs for flowing water; critical depth corresponds to Fr = 1, not zero.

Common Pitfalls:Confusing normal depth (from uniform flow) with critical depth; they coincide only under special conditions.

Final Answer:Agree