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Trapezoidal channel

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A trapezoidal channel made out of brick, with bottom width 6ft and with bottom slope 0.001, is to carry 600cfs. What should be the side slopes and depth of channel for the least number of bricks?

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Please see attached file.

Manning's formula gives flow rate Q as: , where:
= 1.486 (for U.S. units)
n = Manning's roughness coefficient = 0.015 for brick
A = cross section area =
P = cross section wetted ...

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