Critical Depth Calculator & Formula

Calculate critical depth, critical velocity, and minimum specific energy for circular, rectangular, trapezoidal, and triangular sections, where the Froude number equals 1.

Input Parameters

Channel Configuration

Select channel shape and enter geometry

Select the cross-section geometry

cfs

Design flow rate

Channel Geometry

Enter dimensions for the selected shape

ft

Width at channel bottom

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

For educational purposes only. Not a substitute for professional engineering judgment.

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