Summary
A numerical investigation is made of the two-dimensional steady, irrotational flow of a jet of water falling under the influence of gravity, from a channel with an upper wall. This non-linear problem is formulated as an integro-differential equation for the two free surfaces of the jet, via a hodograph transformation, and this equation is then discretized to yield a finite set of non-linear equations which are solved numerically by Newton's method. Physically meaningful solutions are found to exist only for Froude numbers F greater than or equal to a certain critical value F 0, which is to be determined. Results are presented, both for F > F 0 where the detachment is with continuous slope and for F=F 0, where the upper detachment point is a stagnation point at a 120° corner.
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Goh, K.H.M., Tuck, E.O. Thick waterfalls from horizontal slots. J Eng Math 19, 341–349 (1985). https://doi.org/10.1007/BF00042878
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DOI: https://doi.org/10.1007/BF00042878