Biodynamics pp 224-289 | Cite as


  • Y. C. Fung


In the preceding chapters we studied the flow of blood in large blood vessels in which the main feature is a balance between the pressure forces and inertial forces (due to transient acceleration and convective acceleration). Only in the boundary layer are the viscous friction forces important. The boundary layer thickness grows with increasing distance from the entry section, and in a long tube the boundary layer on the wall eventually becomes so thick as to fill the entire tube. The flow is then said to be fully developed. In a fully developed flow, there is an interplay of inertial forces, pressure forces, and viscous forces. In the aorta of man, the length is not sufficient to allow full development of boundary layer ; hence the whole aorta may be considered an entrance region, and the pulse wave can be analyzed approximately by neglecting the viscous stresses. However, arteries divide and divide again. The vessel diameter decreases with each division, and soon the Reynolds number becomes quite small, the entry length becomes only a small multiple of the vessel diameter, and the flow becomes fully developed over most of the length of the vessel. At the same time, the frequency parameter, or the Womersley number, also decreases, so the transient boundary layer also becomes as thick as the tube radius, and the flow becomes in phase with the pressure gradient. Hence, in the smaller arteries the anslysis given in Sec. 3.2 is applicable.


Reynolds Number White Blood Cell Apparent Viscosity Vessel Diameter Blood Vessel Wall 
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© Springer Science+Business Media New York 1984

Authors and Affiliations

  • Y. C. Fung
    • 1
  1. 1.University of CaliforniaSan Diego, La JollaUSA

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