Hostname: page-component-7b7567c8c-7pwfn Total loading time: 0 Render date: 2026-11-14T16:34:19.997Z Has data issue: false hasContentIssue false
  • English
  • Français

Entry flow in a curved pipe

Published online by Cambridge University Press:  29 March 2006

M. P. Singh
M. P. Singh
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of CambridgePermanent address: Department of Mathematics, Indian Institute of Technology, New Delhi.
Get accessRights & Permissions [Opens in a new window]

Abstract

This paper deals with the development of the flow in a curved tube near the inlet. The solution is obtained by the method of matched asymptotic expansions. Two inlet conditions are considered: (i) the condition of constant dynamic pressure at the entrance, which may be of practical interest in applications to blood flow in the aorta; and (ii) a uniform entry condition. It is shown that the geometry and the nature of the entry condition appreciably influence the initial development of the flow. The effect of the secondary flow due to the curvature on the wall shear is discussed and it is shown that the cross-over between shear maxima on the inside and the outside of the tube occurs at a downstream distance which is 1·9 times the radius of the tube for entry condition (i) while in the case of entry condition (ii) it is 0·95 times the radius, which is half the distance required in case (i). It is found that the pressure distribution is not significantly influenced by the secondary flow during the initial development of the motion. The analysis, which is developed for steady motion, can be extended to pulsatile flows, which are of greater physiological interest.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 65 , Issue 3 , 16 September 1974, pp. 517 - 539
Copyright
© 1974 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Adler, M. 1934 Z. angew. Math. Mech. 14, 257.
Barua, S. N. 1963 Quart. J. Mech. Appl. Math. 16, 61.
Caro, C. G., Fitz-Gerald, J. M. & Schroter, R. C. 1969 Nature 223, 1159.
Dean, W. R. 1927 Phil. Mag. 4, 208.
Dean, W. R. 1928 Phil. Mag. 5, 673.
Goldstein, S. 1965 Unpublished work described in Modern Developments in Fluid Dynamics, vol. 1. Dover.
Greenspan, D. 1973 J. Fluid Mech. 57, 167.
Hawthorne, W. R. 1951 Proc. Roy. Soc. A, 206, 374.
Kuchar, N. R. & Ostrach, S. 1967 Unsteady laminar flows in elastic tubes with applications to the vascular system. Case Western Reserve University (Cleveland, Ohio) Rep. FTAS/TR-67–25.Google Scholar
McConaloguje, D. J. & Srivastava, R. S. 1968 Proc. Roy. Soc. A, 307, 37.
McDonald, D. A. 1960 Blood Flow in Arteries. London: Arnold.
Nerem, R. M. & Seed, W. A. 1972 Cardiovascular Res. 6, 1.
Olson, D. E. 1971 Fluid mechanics relevant to respiratory flow within curved or elliptic tubes and bifurcating system. Ph.D. thesis, Imperial College, London.
Pickett, G. F. 1968 Incompressible viscous flow in a curved pipe. Ph.D. thesis, Imperial College, London.
Seed, W. A. & Wood, N. B. 1971 Cardiovascular Res. 5, 319.
Thompson, J. 1876 Proc. Roy. Soc. 28, 5.
Van Dyke, M. 1970 J Fluid Mech 44, 813.
White, C. M. 1929 Proc. Roy. Soc. A, 123, 645.
Wilson, S. D. R. 1971 J. Fluid Mech. 46, 787.
Yao, L. 1973 Entry flow in a curved pipe. Ph.D. thesis, University of California, Berkeley.