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Vertical slender jets

  • James F. Geer (a1) and John C. Strikwerda (a2)
Abstract

The shape of a vertical slender jet of fluid falling steadily under the force of gravity is studied. The problem is formulated as a nonlinear free boundary-value problem for the potential. Surface tension effects are neglected. The use of perturbation expansions results in a system of equations that can be solved by an efficient numerical procedure. Computations were made for jets issuing from orifices in various shapes including an ellipse, a rectangle, and an equilateral triangle. Computational results are presented illustrating the propagation of discontinuities and the formation of thin sheets of fluid.

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Geer, J. F. 1977a Slender streams with gravity: Outer asymptotic expansions I. Phys. Fluids 20, 16131621.
Geer, J. F. 1977b Slender streams with gravity: Outer asymptotic expansions I. Phys. Fluids 20, 16221630.
Geer, J. F. & Keller, J. B. 1979 Slender Streams. J. Fluid Mech. 93, 97115.
Green, A. E. 1977 On the steady motion of jets with elliptical sections. Acta Mech. 26, 171177.
Keller, J. B. & Geer, J. F. 1973 Flows of thin streams with free boundaries. J. Fluid Mech. 59, 417432.
MacCormack, R. W. 1969 The effect of viscosity in hypervelocity impact cratering. A.I.A.A. Hypervelocity Impact Conf., A.I.A.A. Paper no. 69–354.
Rayleigh, Lord 1879 On the capillary phenomena of jets. Proc. Roy. Soc. 29, 7197.
Rayleigh, Lord 1945 The Theory of Sound, 2nd edn. Dover.
Strikwerda, J. C. & Geer, J. F. 1981 A numerical method for computing the shape of a vertical slender jet. S.I.A.M. J. Sci. & Stat. Comp. (to appear).
Tuck, E. O. 1976 The shape of free jets of water under gravity. J. Fluid Mech. 76, 625.
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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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