DrainageCalculators

Critical Depth Calculator

Calculate critical depth for open channels and pipes. Determine the depth at which specific energy is minimum and Froude number equals 1. Supports circular, rectangular, trapezoidal, and triangular sections.

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

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.

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

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Last verified: February 2026