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
- You need critical depth rather than normal depth — Use Critical Depth Calculator
- You already know the depth and need to calculate the flow rate — Use Manning's Channel Calculator
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.
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
| Material | n Value |
|---|---|
| Concrete pipe | 0.012 - 0.015 |
| Corrugated metal pipe | 0.022 - 0.027 |
| HDPE pipe | 0.010 - 0.012 |
| Concrete channel | 0.013 - 0.017 |
| Earth channel (clean) | 0.022 - 0.033 |
| Grass-lined channel | 0.030 - 0.050 |
Source: Chow (1959), HEC-22 Table 7-1.
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Last verified: February 2026