What This Solves
Calculates the critical depth in an open channel or pipe — the depth at which specific energy is minimized and the Froude number equals 1.
Best Used When
- You need to determine the control depth at a channel transition, drop, or free overfall
- You are checking whether flow in a channel or pipe is subcritical or supercritical
- You need critical depth as a boundary condition for water surface profile calculations
Do NOT Use When
- You need the depth at which uniform flow occurs (normal depth) rather than critical depth — Use Normal Depth Calculator
- You only need the Froude number to classify the flow regime — Use Froude Number Calculator
Key Assumptions
- Specific energy (E = y + V²/2g) is minimized at critical depth
- Hydrostatic pressure distribution exists at the cross-section
- Channel slope does not affect critical depth (it depends only on discharge and geometry)
- The cross-section is constant at the location of interest
Input Quality Notes
Critical depth depends only on discharge and channel geometry, not on roughness or slope. Ensure the cross-section dimensions accurately represent the channel at the location of interest.
Critical Depth Overview
Critical depth is the depth at which specific energy is minimum for a given discharge. At critical depth, the Froude number equals 1 and flow transitions between subcritical and supercritical regimes.
Key relationships:
- Critical condition: Fr = V / sqrt(g * Dh) = 1
- Minimum energy: Emin = yc + Vc2/(2g)
- Section factor: Z = A3/2 / T1/2 = Q / sqrt(g)
For rectangular channels: yc = (Q2 / (g * b2))1/3
Design Considerations
- Near-critical flow is unstable - avoid designing for Fr between 0.9 and 1.1
- Critical depth serves as a hydraulic control for flow calculations
- Used to determine if flow is subcritical (y > yc) or supercritical (y < yc)
- Important for hydraulic jump analysis and energy dissipation design
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Last verified: February 2026