Manning Open Channel Flow Calculator

What is the Manning equation?

The Manning equation ties the mean velocity of free surface flow to the shape, slope and surface roughness of the channel: v = (1 / n) × R^(2/3) × S^(1/2). Here n is the Manning roughness coefficient, R the hydraulic radius (flow area divided by wetted perimeter) and S the bed slope. Flow rate is velocity times flow area: Q = v × A. It is used for irrigation channels, storm drains, sewers and stream beds.

Which mode?

With a known depth you get the flow rate. With a known flow rate the calculator finds, numerically, the normal depth that carries it. The section can be rectangular, trapezoidal (triangular when the bottom width is zero) or a partly full circular pipe.

Example

A rectangular concrete channel 2 metres wide runs 1 metre deep with n = 0.013 and a bed slope of 1 per mille. The area is 2 m², the wetted perimeter 4 m and the hydraulic radius 0.5 m. Velocity is 0.63 × 0.0316 / 0.013 = 1.53 m/s and the flow rate 3.06 m³/s. With a Froude number of 0.49 the flow is subcritical.

Limits

The equation is empirical and applies to steady, uniform, fully rough turbulent flow. The n value drives the result directly and is the least certain input: the typical values quoted are approximate. Bends, contractions, weirs and backwater effects, full pressurised flow and freeboard are outside this calculation.