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The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe.
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.
On the contrary to Stokes' paradox, there exists the unsteady-state solution of the same problem which models a fluid flow moving around a circular cylinder with Reynolds number being small. This solution can be given by explicit formula in terms of vorticity of the flow's vector field.
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.
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. At these small Reynolds and Womersley numbers, the viscous effects of the fluid become predominant.
The Reynolds number (Re) is a dimensionless quantity that is commonly used in fluid dynamics and engineering. [6] [7] Originally described by George Gabriel Stokes in 1850, it became popularized by Osborne Reynolds after whom the concept was named by Arnold Sommerfeld in 1908. [7] [8] [9] The Reynolds number is calculated as:
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In fluid dynamics, Prandtl–Batchelor theorem states that if in a two-dimensional laminar flow at high Reynolds number closed streamlines occur, then the vorticity in the closed streamline region must be a constant. A similar statement holds true for axisymmetric flows. The theorem is named after Ludwig Prandtl and George Batchelor.