Channel Flow Calculator

Manning’s equation

Q = (1.486/n) A R^2/3 S^1/2 in US customary units, for steady, uniform flow. Normal depth is the depth at which the equation gives your discharge. Any one of depth, discharge, slope, bottom width (rectangular and trapezoidal) or diameter (pipe) can be solved from the others.

Critical depth and Froude number

Critical depth satisfies Q²T/(gA³) = 1 with g = 32.174 ft/s². The Froude number is V/√(g·A/T); values between 0.86 and 1.13 are flagged because the water surface can be unstable near critical flow (TxDOT Hydraulic Design Manual, Ch. 6). Critical slope is the slope at which your discharge flows at critical depth.

Partly full pipes

A circular section carries its largest open-channel discharge near y/D = 0.938, about 7.6% more than flowing full. Between those two discharges two depths carry the same flow: the lower one is reported with a warning. Above the maximum the pipe would flow under pressure, and the calculator says so instead of giving a depth.

Survey sections and n by segment

Enter station and elevation points from a survey, optionally with an n for each segment. With more than one n, the section is split into panels where n changes and their conveyances are added (subdivision, TxDOT Hydraulic Design Manual, Ch. 6); panel boundaries are not wetted perimeter. The equivalent n and the velocity coefficient α are reported.

Shear

Average boundary shear γRS and maximum bed shear γyS, with γ = 62.4 lb/ft³. Lining stability is checked in the Channel Lining Design Calculator.

Units and numbers

All calculations run in US customary units in your browser; SI values are converted for display. Out-of-range values in a shared link or project file are reported and not used, never adjusted silently.

The calculator is tested against the cases below every time its code changes.

Tolerances: depths and lengths ±0.01 ft or ±0.5%; discharge, velocity, Froude number and slope ±1%; shear ±0.001 lb/ft² or ±1%. Reference programs were run once by HERO E&C and their screen values are kept unchanged. The TxDOT case is the published slope-conveyance example (Figure 7-14).

• Uniform flow only. Backwater, gradually varied flow, transitions, bends, bridges and culverts are not computed.
• Composite roughness along one wetted perimeter (for example a concrete bottom with grass sides) is not combined yet; use a survey section with n by segment, or a single n you have chosen.
• Your city, county or TxDOT may set the roughness, freeboard and design flow to use. Those criteria decide the design.

What is normal depth?

The depth at which steady, uniform flow carries a given discharge in a channel of constant shape, slope and roughness — the depth at which Manning’s equation balances. A real channel reaches it only on a long, uniform reach; near culverts, bridges, drops and confluences the depth is set by gradually varied flow, which this calculator does not compute.

How do I choose Manning’s n?

From a table for the lining and its condition, such as HEC-RAS Table 3-1 (values from Chow, 1959), or by Cowan’s method for natural channels — both in the Manning’s n tool, which carries the value and its source back here. Your local criteria may set the value. In a wide channel a 20% change in n changes the normal depth by about 12%.

What does the Froude number tell me?

Below 1 the flow is subcritical (deeper and slower, controlled from downstream); above 1 it is supercritical (shallow and fast, controlled from upstream). Near 1 the water surface is unstable and wavy, so designs usually stay clear of critical flow.

Can I attach the calculation sheet to a design report?

You can print it and include it as a supporting calculation that you have checked. It is a calculation aid, not a sealed engineering document: the engineer of record reviews it and is responsible for the design, and the criteria of the reviewing agency decide which methods and values apply.