# 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

## Snapshots

## 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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