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A differential equation in fluid mechanics

Published online by Cambridge University Press:  26 February 2010

N. S. Clarke
N. S. Clarke
Affiliation:
The Department of Mathematics, The University of Queensland, Australia.
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Extract

In this paper, solutions of the ordinary non-linear differential equation

are considered. This equation arises in the theory of both axisymmetric and two-dimensional viscous jets falling under gravity. In (1.1), y represents the first approximation to the velocity along the axis of symmetry, and x is a measure of the distance along this axis. Accordingly one of the conditions that the solution must satisfy is, that it cannot have a singularity at a finite value of x. The other condition to be imposed is that y must vanish at x = 0. For a derivation of this equation the reader is referred to Brown [1] or Clarke [2].

Type
Research Article
Information
Mathematika , Volume 13 , Issue 1 , June 1966 , pp. 51 - 53
Copyright
Copyright © University College London 1966

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References

1. Brown, D. R., “A study of the behaviour of a thin sheet of moving liquid”, J. Fluid Mech., 10 (1961), 297.CrossRefGoogle Scholar
2. Clarke, N. S., Ph.D. Thesis (London University, 1966).Google Scholar
3. Ince, E. L., Ordinary Differential Equations (Dover, 1956).Google Scholar