Pulsatile Flow in a Circular Tube
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The velocity distribution, , is computed numerically using NDSolve for a pulsatile pressure-driven flow in a tube. This model considerably simplifies the actual flow through veins and arteries.
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Contributed by: Housam Binous and Brian G. Higgins (March 2011)
Open content licensed under CC BY-NC-SA
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Details
The oscillating pressure-driven flow in a tube obeys the following equations:
-,
ρ,
, ,
, ,
, ,
,
, , , and ,
where , , and are the dimensionless velocity, radial position, and time.
The variable can be considered as a Reynolds number, since it appears as the ratio of inertial forces to viscous forces. There are two characteristic times for this problem: , the period of the imposed pressure gradient, and , the time for diffusion of momentum across the tube.
References
[1] L. G. Leal, Laminar Flow and Convective Transport Processes, Boston: Butterworth–Heinemann, 1992.
[2] L. G. Leal, Advanced Transport Phenomena: Fluid Mechanics and Convective Transport Processes, Cambridge: Cambridge University Press, 2007.
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