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As the Reynolds number increases, smaller and smaller scales of the flow are visible. In a smokestack, the smoke may appear to have many very small velocity perturbations or eddies, in addition to large bulky eddies. In this sense, the Reynolds number is an indicator of the range of scales in the flow.
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.
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 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:
If the Reynolds number is very small, much less than 1, then the fluid will exhibit Stokes, or creeping, flow, where the viscous forces of the fluid dominate the inertial forces. The specific calculation of the Reynolds number, and the values where laminar flow occurs, will depend on the geometry of the flow system and flow pattern.
A turbulence Reynolds number calculated based on the Taylor microscale ... is the root mean square of the velocity fluctuations. The Taylor microscale is given as ...
is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate), is the void fraction of the bed, and; is the particle Reynolds Number (based on superficial velocity [1])..
A key tool used to determine the stability of a flow is the Reynolds number (Re), first put forward by George Gabriel Stokes at the start of the 1850s. Associated with Osborne Reynolds who further developed the idea in the early 1880s, this dimensionless number gives the ratio of inertial terms and viscous terms. [4]