Problem 58374. Classify water surface profiles

Problem statement
Write a function to classify the water surface profile starting at depth y in a channel with longitudinal slope S0, discharge Q, Manning roughness coefficient n, and cross section specified by a structure channelStruct as in Cody Problem 58314. 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 m/s^2 or 32.2 ft/s^2. You can assume that the slopes will be either mild or steep and the profiles will be one of the six shown in the figure below.
Background
Sections of channels are classifying by the relationship between the critical depth yc and the normal depth yn. Slopes with yn < yc are steep—that is, normal flow is supercritical (fast and shallow), whereas slopes with yn > yc are mild—that is, normal flow is subcritical (slow and deep).
The type of water surface profile in gradually varied flow then depends on the water depth y relative to these two depths, as shown in the figure below. Profile S1 has y > yc > yn; profile S2 has yc > y > yn; and profile S3 has yc > yn > y. Profile M1 has y > yn > yc; profile M2 has yn > y > yc; and profile M3 has yn > yc > y.
Figure by NateJonesAR - Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=25698746
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100.0% Correct | 0.0% Incorrect
Last Solution submitted on Jul 11, 2023

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