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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 ...
Stokes' law makes the following assumptions for the behavior of a particle in a fluid: Laminar flow; No inertial effects (zero Reynolds number) Spherical particles; Homogeneous (uniform in composition) material; Smooth surfaces; Particles do not interfere with each other.
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 turbulent flow in a fluid is defined by the critical Reynolds number, for a closed pipe this works out to approximately R e c ≈ 2000. {\displaystyle \mathrm {Re} _{\text{c}}\approx 2000.} In terms of the critical Reynolds number, the critical velocity is represented as
A particle with a low Stokes number follows fluid streamlines (perfect advection), while a particle with a large Stokes number is dominated by its inertia and continues along its initial trajectory. In the case of Stokes flow , which is when the particle (or droplet) Reynolds number is less than about one, the particle drag coefficient is ...
The specific particle Reynolds number of interest is called the boundary Reynolds number, and it is formed by replacing the velocity term in the particle Reynolds number by the shear velocity, , which is a way of rewriting shear stress in terms of velocity.
where: = (), = = (), is the modified Reynolds number, is the packed bed friction factor,; is the pressure drop across the bed,; is the length of the bed (not the column), is the equivalent spherical diameter of the packing,
The particle Reynolds number Re p would be used for particle suspended in flowing fluids, for example. As with flow in pipes, laminar flow typically occurs with lower Reynolds numbers, while turbulent flow and related phenomena, such as vortex shedding , occur with higher Reynolds numbers.