Calculate open-channel or pipe flow with Manning’s equation from shape, size, depth and slope, using typical roughness n values or your own.

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Manning's Flow Formula

Manning’s equation estimates steady uniform open-channel discharge. In US customary units, a commonly rounded coefficient is 1.486; SI uses 1. The calculator computes in SI and converts the result.

Q = (1.486/ n) * A * R(2/3) * √(s)

  • Where Q is the Manning flow rate (ft3/s)
  • n is the roughness coefficient
  • A is the flow area (ft2)
  • R is the hydraulic radius (ft)
  • s is the energy slope (ft/ft), approximated by bed slope only for suitable uniform flow

What is Manning's Flow?

Manning's flow is a metric of the volumetric flow rate of water moving through an open channel. The volumetric flow rate is calculated using Manning's Equation which is stated above.

The equation itself was developed as an alternative to the Chezy Equation for flow through channels to try and achieve more accurate calculations.

How to calculate Manning's Flow?

The following example outlines how to calculate open channel flow using Manning's Equation.

First, determine the roughness coefficient. This is typically gathered through tables. For this example, the coefficient is .040.

Next, determine the flow area. In this example, the area is 20 ft2.

Next, determine hydraulic radius as flow area divided by wetted perimeter. Use 1 ft for this example.

Next, determine the slope of the channel. Use an energy slope of 0.005 ft/ft (0.5%) for this example.

Finally, calculate the flow rate using the formula:

Q = (1.486/ n) * A * R(2/3) * √(s)

Q = (1.486/ .040) * 20 * 1(2/3) * √(0.005)

Q ≈ 52.538 ft3/s

FAQ

What is the significance of the roughness coefficient in Manning's Equation?
The roughness coefficient (n) in Manning's Equation accounts for the internal friction within the channel that affects the flow rate. Different materials and surface textures have different coefficients, reflecting how they impede water flow. This value is crucial for accurately calculating the flow rate.

How does the hydraulic radius affect the flow rate in an open channel?
The hydraulic radius (R), which is the ratio of the flow area to the wetted perimeter, directly influences the flow rate in Manning's Equation. A larger hydraulic radius indicates a more efficient cross-section for flow, leading to a higher flow rate. It's a key factor in determining how easily water can move through a channel.

Why is Manning's Equation preferred over the Chezy Equation for calculating flow in open channels?
Manning's Equation is a convenient empirical model for suitable open-channel flows. Its accuracy depends on geometry, energy slope, roughness selection and uniform-flow assumptions; backwater, near-crown waves and pressurization require further analysis. A circular conduit can have two mathematical depths near full flow; the calculator uses the lower depth as primary and labels the upper mathematical branch when present.