Given:
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theta = interior angle in radians
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d = diameter
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y = depth
In computing the theta for circular sections, there are three conditions to deal with.
The maximum flow capacity in circular sections occurs at a depth of 0.938 times the diameter, however, it is common to design circular conduits to carry maximum flows when flowing full at 100% of the diameter. Wave action and irregularities make it difficult to maintain flows at 0.938 times the diameter for very long. The flow is unstable at that depth.