DrainageCalculators

Normal Depth Calculator

Calculate normal depth for open channels and pipes using Manning's equation. Iteratively solve for the depth at which uniform flow occurs. Supports circular, rectangular, trapezoidal, and triangular sections.

What This Solves

Iteratively solves Manning's equation to find the normal depth — the depth at which uniform flow occurs in an open channel or pipe for a given discharge, slope, and roughness.

Best Used When

  • You need to find the equilibrium flow depth in a long channel or pipe at a given discharge
  • You are checking whether a channel will overtop its banks at the design flow
  • You need normal depth as a boundary condition for water surface profile calculations

Do NOT Use When

Key Assumptions

  • Uniform flow conditions exist (depth and velocity are constant along the channel)
  • The channel has a constant slope, roughness, and cross-section
  • The energy grade line slope equals the channel bed slope
  • Flow is fully turbulent (Manning's equation is applicable)

Input Quality Notes

Normal depth is very sensitive to Manning's n and channel slope. Small errors in these inputs produce significant changes in depth. Verify roughness values against field conditions.

Input Parameters

Channel Configuration

Select channel shape and enter geometry

Select the cross-section geometry

cfs

Target flow rate

Flow Parameters

Enter slope and roughness

ft/ft

Longitudinal bed slope (ft/ft or m/m)

Roughness coefficient

Channel Geometry

Enter dimensions for the selected shape

ft

Width at channel bottom

Normal Depth Overview

Normal depth is the depth at which uniform flow occurs in an open channel. At normal depth, the energy slope equals the channel bed slope, meaning gravitational forces are balanced by frictional resistance.

Manning's equation for uniform flow:

  • US Units: Q = (1.486/n) * A * R2/3 * S1/2
  • SI Units: Q = (1/n) * A * R2/3 * S1/2

This calculator iteratively solves for the depth that satisfies Manning's equation for the given discharge.

Typical Manning's n Values

Materialn Value
Concrete pipe0.012 - 0.015
Corrugated metal pipe0.022 - 0.027
HDPE pipe0.010 - 0.012
Concrete channel0.013 - 0.017
Earth channel (clean)0.022 - 0.033
Grass-lined channel0.030 - 0.050

Source: Chow (1959), HEC-22 Table 7-1.

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Last verified: February 2026