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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.
The Womersley number is normally written in the powerless form = (). In the cardiovascular system, the pulsation frequency, density, and dynamic viscosity are constant, however the Characteristic length , which in the case of blood flow is the vessel diameter, changes by three orders of magnitudes (OoM) between the aorta and fine capillaries.
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] =, Or considering both equations,
Blood flow in small vessels, such as capillaries, is characterized by small Reynolds and Womersley numbers. A vessel of diameter of 10 µm with a flow of 1 millimetre/second , viscosity of 0.02 poise for blood, density of 1 g/cm 3 and a heart rate of 2 Hz , will have a Reynolds number of 0.005 and a Womersley number of 0.0126.
The flow profiles was first derived by John R. Womersley (1907–1958) in his work with blood flow in arteries. [1] The cardiovascular system of chordate animals is a very good example where pulsatile flow is found, but pulsatile flow is also observed in engines and hydraulic systems , as a result of rotating mechanisms pumping the fluid.
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John Ronald Womersley (20 June 1907 – 7 March 1958) was a British mathematician and computer scientist who made important contributions to computer development, and hemodynamics. [1] Nowadays he is principally remembered for his contribution to blood flow , fluid dynamics and the eponymous Womersley number , a dimensionless parameter ...
The Dean number (De) is a dimensionless group in fluid mechanics, which occurs in the study of flow in curved pipes and channels.It is named after the British scientist W. R. Dean, who was the first to provide a theoretical solution of the fluid motion through curved pipes for laminar flow by using a perturbation procedure from a Poiseuille flow in a straight pipe to a flow in a pipe with very ...