How to use the manning equation open channel flow calculator
- Choose the channel shape: rectangular, trapezoidal or a circular pipe flowing part full.
- Choose meters (SI) or feet and inches.
- Enter the Manning roughness n, the slope as a decimal, the dimensions of the channel and the flow depth.
- Read the flow rate, velocity, flow area, wetted perimeter, hydraulic radius, top width and Froude number.
Formula
Velocity v = (k / n) x R^(2/3) x S^(1/2), with k = 1 for SI units and k = 1.486 for feet
Hydraulic radius R = flow area / wetted perimeter
Flow rate Q = v x flow area
Froude number Fr = v / sqrt(g x flow area / top width)
A Froude number below 1 means subcritical flow, which is calm and controlled from downstream. Above 1 the flow is supercritical, fast and shallow, and it is controlled from upstream.
A rectangular channel 2 m wide and 1 m deep
With a roughness n of 0.013, a slope of 0.001, a bottom width of 2 m and a depth of 1 m, the flow area is 2 square meters and the wetted perimeter is 2 + 2 x 1 = 4 m. The hydraulic radius is 0.5 m.
The velocity is (1 / 0.013) x 0.5^(2/3) x 0.001^(1/2) = 1.5324 m/s, so the flow rate is 3.0648 cubic meters per second, or 3064.8 liters per second. The top width is 2 m and the Froude number is 0.4893, which is subcritical flow.
Choosing n and the slope
The roughness coefficient n depends on the lining. Smooth concrete is lower than rough earth or a channel with weeds, and the value on the page is only an example. Use a reference for your surface, and remember that real channels are often rougher than the clean value.
The slope is the drop divided by the length, as a decimal, so 1 m in 1,000 m is 0.001. For a drain that carries the flow, see the French drain calculator.
Partly full pipes
For a circular pipe the page works out the area and wetted perimeter of the segment filled to the depth you enter. A pipe flowing about 80 to 95 percent full carries a little more than a pipe that is full, because the wetted perimeter grows quickly near the top.
For pressurized pipes that run completely full, use the Hazen-Williams calculator instead. To turn a flow into a volume over time, use the flow rate calculator.
Assumptions and limits
- Flow is steady and uniform, with a constant slope, shape and roughness along the channel.
- Slope is the slope of the channel bed, which equals the water surface slope in uniform flow.
- Roughness values are examples. Use values for your own lining and condition.
- Depth cannot exceed the pipe diameter for circular shapes.
Frequently asked questions
What is the Manning equation used for?
It estimates the speed and flow of water in an open channel, such as a ditch, a culvert flowing part full or a gutter, from its shape, slope and roughness.
What does the Froude number tell me?
It compares the flow speed with the speed of a surface wave. Below 1 the flow is calm and subcritical. Above 1 it is fast and supercritical.
Why is the US constant 1.486?
It converts the formula to feet. The SI form has a constant of 1, and the US form multiplies by 1.486 to give the same result in feet per second.
Can I find the depth for a given flow?
Not directly. Change the depth until the flow rate matches the flow you need. The flow rises steadily with depth, so a few trials are enough.