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Unsteady flow of a viscous fluid from a source in a wall

  • E. O. Tuck (a1)


A problem with possible physiological applications concerns the escape of a viscous fluid through a small hole in a wall. The solution presented here is for a line source of sinusoidally pulsating strength located at the origin x = y = 0, where the plane y = 0 is a rigid wall and the fluid is at rest at y = + ∞. The linearized Navier—Stokes equations are solved, and results in the form of streamline plots are shown and discussed.



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Fry, D. L. & Greenfield, J. C. 1963 The mathematical approach to hemodynamics, with particular reference to Womersley's theory. Pulsatile Blood Flow (ed. E. O. Attinger). Ch. 4. New York: McGraw-Hill.
Rayleigh, Lord 1893 On the flow of viscous liquids, especially in two dimensions. Phil. Mag. (5), 36, 354.
Tuck, E. O. 1969 Transmission of water waves through small apertures. (Unpublished.)
Wang, C.-Y. 1966 The resistance on a circular cylinder in an oscillating stream. Quart. Appl. Math. 23, 305.
Womersley, J. R. 1955 Oscillatory motion of a viscous liquid in a thin-walled elastic tube. I. The linear approximation for long waves. Phil. Mag. 46, 199.
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