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The Womersley number (or ) is a dimensionless number in biofluid mechanics and biofluid dynamics. It is a dimensionless expression of the pulsatile flow frequency in relation to viscous effects . It is named after John R. Womersley (1907–1958) for his work with blood flow in arteries . [ 1 ]
The Reynolds and Womersley Numbers are also used to calculate the thicknesses of the boundary layers that can form from the fluid flow’s viscous effects. The Reynolds number is used to calculate the convective inertial boundary layer thickness that can form, and the Womersley number is used to calculate the transient inertial boundary thickness that can form.
is the dimensionless Womersley number, ω: is the angular frequency of the first harmonic of a Fourier series of an oscillatory pressure gradient, n: are the natural numbers, P' n: is the pressure gradient magnitude for the frequency nω, ρ: is the fluid density, μ: is the dynamic viscosity, R: is the pipe radius, J 0 (·)
Dimensionless numbers (or characteristic numbers) have an important role in analyzing the behavior of fluids and their flow as well as in other transport phenomena. [1] They include the Reynolds and the Mach numbers, which describe as ratios the relative magnitude of fluid and physical system characteristics, such as density, viscosity, speed of sound, and flow speed.
The Strouhal number is used as a ratio of the Deborah number (De) and Weissenberg number (Wi): [9] =. The Strouhal number may also be used to obtain the Womersley number (Wo). The case for blood flow can be categorized as an unsteady viscoelastic flow, therefore the Womersley number is [9]
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