How to Solve Manning's Equation for Depth of Flow of Circular Pipe

Written by thomas bourdin
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How to Solve Manning's Equation for Depth of Flow of Circular Pipe
Manning's equation can help engineers understand flow through water channels. (Jupiterimages/ Images)

Manning's equation, named after 19th century engineer Robert Manning, is an empirical relationship that relates uniform flow in an open channel to the channel velocity and slope and the flow area. This equation has many applications in the fields of geological and civil engineering, such as in flood control and planning. Manning's equation applies to many different physical settings, such as a circular pipe.

Skill level:


  1. 1

    Convert the depth of flow of the circular pipe to a hydraulic radius. Although this can be complicated, there are conversion tables that can be used for this task. As an example, if a pipe 1 meter in diameter has a flow depth of 0.2 meters, the hydraulic radius is 0.121 meters.

  2. 2

    Square the hydraulic radius (i.e., multiply the number by itself) and take the cube root of the result. Continuing the example, the square root of 1.21 is 1.46, and the cube root of that number is 1.14. Call this number result A.

  3. 3

    Determine the square root of the slope of the channel. For example, if the slope is 4 feet per foot (i.e., the channel increases 4 feet vertically for every 1 foot horizontally), the square root of this number is 2. Call this result B.

  4. 4

    Multiply flow area by results A and B. Continuing the example, multiplying a flow area of 6 square feet by 2 and 1.14 gives 13.68. Call this result C.

  5. 5

    Divide result C by Manning's Roughness Coefficient, a constant determined by the type of channel, to find the flow rate. If the channel in the example is a clean, straight channel with no deep pools or edges, the Manning Roughness Coefficient is 0.03, which will give a flow rate in the channel of 456 cubic feet per second.

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