Problem 58314. Compute the normal depth of a channel
For steady uniform flow in a channel of constant cross section and slope, the depth does not change with distance or time. In this state, the component of the fluid’s weight down the slope is balanced by the friction from the wetted perimeter $P$, the portion of the perimeter touched by the fluid.
As described in Cody Problem 57969, the normal depth, or depth of flow in this state, can by computed from Manning’s equation for the discharge (or flow) Q):
where n is Manning’s roughness coefficient, is the hydraulic radius, is the slope of the channel, and A is the cross-sectional area of the flow. The coefficient C is 1 for SI units and 1.49 for U.S. customary units.
Write a function to compute the normal depth of a channel. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system). The geometry of the channel’s cross section will be specified by a structure channelStruct with the following fields and possible values:
The side slope is the horizontal distance divided by the vertical distance; for example, a side slope of 1.5 would mean the bank rises 1 m for every 1.5 m in the horizontal direction.
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3 Comments
Christian Schröder
on 17 May 2023
I'm really enjoying these CE372 problems. Keep 'em coming!
William
on 18 May 2023
Not sure I understand! It seems that the "correct" result for the normal height in test problems 9, 10 are both larger than the radius of the channel. That can't be right, can it?
ChrisR
on 18 May 2023
My diagram probably confused you, William. Both of those cases are closed conduits: test 9 is a circular culvert, and test 10 is a circular pipe.
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