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The particle Reynolds number is important in determining the fall velocity of a particle. When the particle Reynolds number indicates laminar flow, Stokes' law can be used to calculate its fall velocity or settling velocity. When the particle Reynolds number indicates turbulent flow, a turbulent drag law must be constructed to model the ...
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 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 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:
The general form for the Reynolds number flowing through a tube of radius r (or diameter d): = = where v is the velocity of the fluid, ρ is its density, r is the radius of the tube, and μ is the dynamic viscosity of the fluid. A turbulent flow in a fluid is defined by the critical Reynolds number, for a closed pipe this works out to approximately
C L is a function of the angle of the body to the flow, its Reynolds number and its Mach number. The section lift coefficient c l refers to the dynamic lift characteristics of a two-dimensional foil section, with the reference area replaced by the foil chord. [1] [2]
The theory of the Reynolds stress is quite analogous to the kinetic theory of gases, and indeed the stress tensor in a fluid at a point may be seen to be the ensemble average of the stress due to the thermal velocities of molecules at a given point in a fluid. Thus, by analogy, the Reynolds stress is sometimes thought of as consisting of an ...
Skin friction drag is generally expressed in terms of the Reynolds number, which is the ratio between inertial force and viscous force. Total drag can be decomposed into a skin friction drag component and a pressure drag component, where pressure drag includes all other sources of drag including lift-induced drag . [ 1 ]