Optimization of an Open Circular Channel

by Sebastian Hagn

Submitted : Spring 2011

Culverts, sewers and canals are examples of open channel flow, in which water is flowing through a channel with its surface exposed to the atmosphere. These channels come in various shapes. A common shape is a circular cross section as shown below. Drag in a channel occurs because the fluid has a zero velocity at each solid surface. Therefore, the most efficient channel is one for which, for a given cross sectional area of flow A, the wetted perimeter P is a minimum. Wetted perimeter is the part of the perimeter of the cross section that is in contact with liquid. Suppose a circular channel is to have a cross sectional flow area of 4 m². Find the value of the radius r that will provide the most efficient channel.

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