On the question of the shape of a free jet in the discharge of an ideal fluid from a vessel with plane walls
Abstract
The question of the shape of a free jet in the discharge of an ideal fluid from a vessel, when the motion takes place in a plane, was first solved by Helmholtz for the case of fluid outflow through a channel projecting into this vessel. Helmholtz's method was then generalized by Kirchhoff, who provided solutions to several problems related to plane fluid motion, including, among others, the problem of fluid outflow through a slit in a plane wall. Both of these problems are discussed by Lamb in his treatise on hydrodynamics, where he applies the method of conformal transformation by Schwarz and Christoffel to derive the equation of the free jet. The purpose of this present note is to apply this same method to derive the equation of the free jet for fluid outflow through an opening in a vessel with plane walls, where the walls converge towards the opening at an angle of 2α.
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References
- Monthly Reports of the Berlin Academy, April 1868.
- Crelle's Journal for Pure and Applied Mathematics, 70, 1869.
- Lamb: Textbook of Hydrodynamics, 1907. Page 110.
- Schwarz: "On Some Mapping Problems", Crelle's Journal, 70.