Manning's Equation Calculator: Open Channel and Part-Full Pipe Flow, Velocity, Flow Rate and Depth

Find the flow in a drain, a channel or a part-full gravity pipe, or the depth at which a given flow runs.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose a rectangular, trapezoidal or circular channel and enter its size, the slope of the bed and the Manning roughness n.

For the flow case, enter the depth. The calculator finds the area, wetted perimeter, hydraulic radius, the velocity V = R to the two thirds times root S over n, the flow rate and the Froude number.

For the depth case, enter the flow and it finds the depth by iteration. For a pipe it also gives the full-pipe flow and the percentage of it.

Formulas used

  • V = \frac{1}{n}R^{2/3}S^{1/2}
  • R = \frac{A}{P}
  • Q = VA
  • \mathrm{Fr} = \frac{V}{\sqrt{gA/T}}

Worked example

With the default numbers in the calculator above:

  1. Flow area and wetted perimeter: 2.00 m2 and 4.00 m
  2. Hydraulic radius (area over wetted perimeter): 0.50 m
  3. Velocity (Manning's equation): 1.53 m/s
  4. Flow rate: 3.06 m3/s (3064.78 L/s)
  5. Froude number: 0.49 (subcritical, a calm flow controlled from downstream)

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Shape of the channel Circular pipe, part full; Depth of flow (for the flow case) 0.3 m.

  1. Flow area and wetted perimeter: 0.14 m2 and 0.94 m
  2. Hydraulic radius (area over wetted perimeter): 0.15 m
  3. Velocity (Manning's equation): 0.69 m/s
  4. Flow rate: 0.0971 m3/s (97.08 L/s)
  5. Froude number: 0.45 (subcritical, a calm flow controlled from downstream)
  6. Flow when the pipe runs full: 194.17 L/s; the flow now is 50.00 percent of the full flow, at 50.00 percent of the depth

Common questions

What is the hydraulic radius?

The flow area divided by the wetted perimeter, which is the length of the channel that touches the water. It is not the same as the geometric radius.

What velocity should a stormwater pipe have?

Enough to clean itself, above about 0.6 to 0.75 m/s, but not so fast that it erodes, below about 6 m/s for a pipe.

When can I use Manning's equation?

For steady, uniform, gravity flow. It does not apply to a pressurised pipe or to a flow that is changing quickly.

What is Froude number?

The ratio of the flow velocity to the speed of a wave on the water. Under 1 the flow is calm (subcritical); over 1 it is fast (supercritical).

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Chow, Open-Channel Hydraulics; Australian Rainfall and Runoff (drainage design); AS/NZS 3500.3 Stormwater drainage.

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