Problem 58324. Compute the critical depth of a channel
Write a function to compute the critical depth of a channel with discharge Q. The unit system will be specified in units as either ‘SI’ or ‘USCS’ (U.S. customary system); take the acceleration of gravity g to be either 9.81 or 32.2 . The geometry of the channel’s cross section will be specified by a structure channelStruct as in Cody Problem 58314.
Specific energy for a flow is , where y is the water depth and V is the velocity averaged over the cross section. The critical depth is the depth of minimum specific energy. Using the definition of the average velocity and differentiating with respect to depth gives
Then using the definition of the top width gives the condition for the critical depth in terms of a dimensionless parameter called the Froude number :
Flows with depths smaller than critical are supercritical—fast and shallow (), and flows with depths greater than critical are subcritical—deep and slow (). A flow changes from supercritical to subcritical with a hydraulic jump, which can be observed in the field, in the laboratory, and even in a kitchen sink.
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