Maximum Flow Rate in Open-Channel Flow for a Circular Pipe
Introduction
This application determines the greatest attainable water flow rate in a partially filled circular pipe.
It uses the Manning formula to determine the flow rate in the open-channel flow of water:
where:
Q is the flow rate
n is an empirical coefficient
A is the cross-sectional area of flow
R is the hydraulic radius
S0 is the incline of the channel
An equation that represents the hydraulic radius of a partially filled circular pipe is derived and substituted into the Manning formula. The resulting equation is then optimized to find the maximum flow rate.
Manning Formula for a Circular Pipe
Manning formula:
For a partially filled circular pipe, the flow area (the blue shaded area in the preceding diagram) is:
The wetted perimeter is given by the following formula.
Hence, the hydraulic radius, R, is:
The Manning formula then becomes:
Maximum Flow Rate for a Circular Pipe
Pipe radius:
Incline of the channel:
Roughness coefficient:
The maximum flow rate is...
...when is ...
... and the flow depth is:
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