The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube

Wu Wang-yi; Richard Skalak

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Wu Wang-yi, Richard Skalak. The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube[J]. Applied Mathematics and Mechanics, 1983, 4(6): 743-756.

Citation:

Wu Wang-yi, Richard Skalak. The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube[J]. Applied Mathematics and Mechanics, 1983, 4(6): 743-756.

Citation:

Wu Wang-yi, Richard Skalak. The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube[J]. Applied Mathematics and Mechanics, 1983, 4(6): 743-756.

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The Creeping Motion in the Entry Region of a Semi-Infinite Circular Cylindrical Tube

Wu Wang-yi¹,
Richard Skalak²

1.
Department of Mechanics, Peking University, Beijing;
2.
Department of Civil Engineering and Engineering Mechanics, Bioengineering Institute, Columbia University, New York

Received Date: 1983-01-18
Publish Date: 1983-12-15

Abstract

Abstract

In 1969, Lew and Fung^[1] considered the inlet flow into a semi-infinite circular cyfinder at low Reynolds mumber Dagan, et al.^[2] in 19$Z obtained a series solution for the creeping motion through a pore of finite length directly The numerical results oblained in[1]also describe the entrance flow in tube of a finite length, because the Fourier integrals in the general solutions are replaced by Fourier series.In the present paper, the Fourier integrals are evaluated numerically and the velocity, pressure distribution and the stream function in the entry region of a semi-infinite circular cylindrical tube for a uniform entry velocity are obtained more preciselp.The corresponding inlet length which is equal to (1,2) times the radius of the tube is close to the factor (1.3) suggested hyLew and Fung.^[1] The collucation technique applied in the present paper is shown to converge rapidly and it should be useful in other similar problems.

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References(9)

References

[1]	Lew, H.S and Y, C, Fung, J.Biomechamcs, 2(1969).105-119.
[2]	Dagan, Z.,S.Weinbaum and R, Pfeffer, J,Fluid Mech.,115(1982),502-523.
[3]	Goldstein, S, (ed),Modern Developments in Fluid Mechanics,1(1938),299-311.
[4]	Rosenhead, L.(ed.), Laminar Boundary Layers, Oxford University Press, London,(1963).
[5]	Schlichting, H.,Boundary Layer Theory, 4th Edition, McGraw-Hill, New York(1962).168.
[6]	Gluckman, M, J.,S, Weinbaum and R, Pfeffer, J.Fluid 147ech,55 (1972).677-709.
[7]	Stimson, M, and O,B.Jeffery, Proc, Roy.Soc.,A11]1, 110(1926).
[8]	Rabinowitz, P and G, weiss, MTAG, 13(1959).285-293.
[9]	Happel, J.and H, Brenner, Low Reynolds Number Hydrodynamics, 2nd Edition,Noordhoff International Publishing, Leyden, (1973).