Pressure Wave Propagation in Fluid-Filled Co-Axial Elastic Tubes Part 1: Basic Theory

[+] Author and Article Information
K. Berkouk, P. W. Carpenter, A. D. Lucey

Fluid Dynamics Research Center, University of Warwick, Coventry CV4 7AL, UK

J Biomech Eng 125(6), 852-856 (Jan 09, 2004) (5 pages) doi:10.1115/1.1634280 History: Received November 01, 2002; Revised May 19, 2003; Online January 09, 2004
Copyright © 2003 by ASME
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Grahic Jump Location
A schematic sketch of the theoretical model based on co-axial flexible tubes: (a) end view; (b) side view. When applied to the intraspinal CSF system, the space A between the outer rigid and the inner flexible one represents the spinal subarachnoid space, the space B within the inner tube represents the central canal (or alternatively the spinal-cord tissue), and the flexible tube represents the spinal cord (or alternatively the pia mater). The alternative interpretations of space B and the flexible tube are discussed in Part 2 of the present paper.
Grahic Jump Location
A schematic illustration showing the propagation of a pressure pulse along the co-axial flexible tube system: (a) a wave diagram showing that the leading edge of the pulse steepens with time to form an elastic jump; (b) the initial form of the tube-wall displacement at time t=0; (c) the form of the tube-wall displacement at time t=t1.
Grahic Jump Location
The variation of dimensionless wave speed with area ratio. Note that the wave speed doubles in value when the area ratio changes from αx to αy, thereby illustrating the sensitivity of wave speed to relatively small displacements of the flexible tube wall.
Grahic Jump Location
A schematic sketch showing the control volume for deriving the relationships between conditions before and after an elastic jump propagating along the co-axial flexible tube system.




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