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On the flow of an elastico-viscous liquid in a curved pipe of elliptic cross-section under a pressure-gradient

Published online by Cambridge University Press:  28 March 2006

R. H. Thomas  and
K. Walters
R. H. Thomas
Affiliation:
Welsh College of Advanced Technology, Cardiff
K. Walters
Affiliation:
University College of Wales, Aberystwyth
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Abstract

Consideration is given to the flow of an elastico-viscous liquid in a curved pipe under a pressure gradient. The cross-section of the pipe is an ellipse, the axes of which are in an arbitraty position with respect to the radius of curvature of the pipe. The method of solution is an extension of that used by Dean (1927) and by Thomas & Walters (1963) in their consideration of flow through a curved pipe of circular cross-section.

It is shown that the liquid elements move along the pipe in two sets of spirals. When the axes of the ellipse are in an asymmetrical position the streamline projections on the cross-section of the pipe are strongly dependent on the elasticity in the liquid. This is not so when the axes are in a symmetrical position. However, in this case, the pitch of the spirals is strongly dependent upon the elasticity of the liquid.

It is also shown that the flux through the pipe is independent of the curvature of the pipe to first order in the curvature.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 21 , Issue 1 , January 1965 , pp. 173 - 182
Copyright
© 1965 Cambridge University Press

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References

Dean, W. R. 1927 Phil. Mag. 4, 208.
Dean, W. R. 1928 Phil. Mag. 5, 673.
Oldroyd, J. G. 1950 Proc. Roy. Soc. A, 200, 523.
Thomas, R. H. & Walters, K. 1963 J. Fluid Mech. 16, 228.
Walters, K. 1960 Quart. J. Mech. Appl. Math. 13, 444.
Walters, K. 1964 Second-Order Effects in Elasticity, Plasticity and Fluid Dynamics, p. 507. London: Pergamon Press.