Skip to main content Accessibility help
×
Home

The flow due to an oscillating piston in a cylindrical tube: a comparison between experiment and a simple entrance flow theory

  • J. H. Gerrard (a1) and M. D. Hughes (a1)

Abstract

The velocity on the axis of a circular tube was measured over a range of distances from a piston reciprocating in simple harmonic motion. These velocities become independent of axial distance sufficiently far from the piston. The method of calculating the developing flow is based on a comparison with steady laminar flow which, in the entry region of a circular tube, approaches the fully developed state exponentially with distance x from the entry. The steady flow is a function of xν/R2u0 where ν is the kinematic viscosity, R is the tube radius and u0 is the entry velocity. It is shown that within the limits of experimental error, an oscillating flow follows the steady flow development if u0 is the instantaneous entry velocity and if the characteristic length is changed from R to the oscillating boundary-layer thickness in the established flow.

Copyright

References

Hide All
Atabek, H. B. & Chang, C. C. 1961 Oscillating flow near the entry of a circular tube Z. angew. Math. Phys. 12, 185.
Atabek, H. B., Chang, C. C. & Fingerson, L. M. 1964 Measurement of laminar oscillatory flow in the inlet length of a circular tube. Physics in Med. & Biol. 9, 219.
Avula, X. J. R. 1969a A combined method for determining the velocity of starting flow in a long circular tube. J. Phys. Soc. Japan, 21, 497.
Avula, X. J. R. 1969b Analysis of suddenly started laminar flow in the entrance region of a circular tube. Appl. Sci. Res. 21, 248.
Baker, D. J. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573.
Campbell, W. D. & Slattery, J. C. 1963 Flow in the entrance of a tube. Trans. A.S.M.E. J. Basic Engng. 85, 41.
Cerny, L. C. & Walawender, W. P. 1966 The flow of a viscous liquid in a converging tube. Bull. Math. Biophys. 28, 11.
Davis, W. & Fox, R. W. 1967 An evaluation of the hydrogen bubble technique for the quantitative determination of fluid velocities within clear tubes. Trans. A.S.M.E. J. Basic Engng 89, 771.
Florio, P. J. & Mueller, W. K. 1968 Development of a periodic flow in a rigid tube. Trans A.S.M.E. J. Basic Engng 90, 395.
Gerrard, J. H. 1971a An experimental investigation of pulsating turbulent water flow in a tube. J. Fluid Mech. 46, 43.
Gerrard, J. H. 1971b Velocity measurement in water using flow visualisation by tracers shed from a wire. To be published.
Harris, J., Peer, G. & Wilkinson, W. L. 1969 Velocity profiles in laminar oscillating flow in tubes. J. Phys. E. J. Sci. Instrum. 2, 913.
Linford, R. G. & Ryan, N. W. 1965 Pulsatile flow in rigid tubes. J. Appl. Physiol. 20, 1078.
Mcdonald, D. A. 1960 Blood flow in arteries. London: Edward Arnold.
Schlichting, H. 1968 Boundary Layer Theory, 6th edn. Pergamon.
Schraub, F. A., Kline, S. J., Henry, J., Runstadler, P. W. & Littell, A. 1965 Use of hydrogen bubbles for quantitative determination of time-dependent velocity fields in low speed water flows. Trans A.S.M.E. J. Basic Engng 87, 429.
Sparrow, E. M., Lin, S. H. & Lundgren, T. S. 1964 Flow development in the hydrodynamic entrance region of tubes and ducts. Phys. Fluids, 7, 338.
Tabacynski, R. J., Hoult, D. P. & Keck, J. C. 1970 High Reynolds number flow in a moving corner. J. Fluid Mech. 42, 249.
Uchida, S. 1956 The pulsating viscous flow superposed on the steady laminar motion of incompressible fluid in a circular pipe. Z. angew Math. Phys. 7, 403.
Womersley, J. R. 1955 Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known. J. Physiol. 127, 553.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

The flow due to an oscillating piston in a cylindrical tube: a comparison between experiment and a simple entrance flow theory

  • J. H. Gerrard (a1) and M. D. Hughes (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.