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In that case the equivalent spherical diameter corresponds to the equivalent sieve diameter, or the diameter of a sphere that just passes through a defined sieve pore. Of note, the equivalent sieve diameter can be significantly smaller than the area-equivalent diameter obtained by optical methods, as particles can pass the sieve apertures in an ...
This is equivalent to the above definition of the 2D mean diameter. However, for historical reasons, the hydraulic radius is defined as the cross-sectional area of a pipe A , divided by its wetted perimeter P , which leads to D H = 4 R H {\displaystyle D_{\text{H}}=4R_{\text{H}}} , and the hydraulic radius is half of the 2D mean radius.
is the equivalent spherical diameter of the packing, is the density of fluid, is the dynamic viscosity of the fluid, is the superficial velocity (i.e. the velocity that the fluid would have through the empty tube at the same volumetric flow rate),
Several kinds of object can be measured by equivalent diameter, the diameter of a circular or spherical approximation to the object. This includes hydraulic diameter, the equivalent diameter of a channel or pipe through which liquid flows, and the Sauter mean diameter of a collection of particles. The diameter of a circle is exactly twice its ...
For a fully filled duct or pipe whose cross-section is a convex regular polygon, the hydraulic diameter is equivalent to the diameter of a circle inscribed within the wetted perimeter. This can be seen as follows: The N {\displaystyle N} -sided regular polygon is a union of N {\displaystyle N} triangles, each of height D / 2 {\displaystyle D/2 ...
In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are These are the radial distance r along the line connecting the point to a fixed point called the origin ;
is the sphericity of the particles in the packed bed (= 1.0 for spherical particles); d p {\displaystyle d_{\mathrm {p} }} is the diameter of the volume equivalent spherical particle; V 0 {\displaystyle V_{\mathrm {0} }} is the superficial or "empty-tower" velocity which is directly proportional to the average volumetric fluid flux in the ...
Defined by Wadell in 1935, [1] the sphericity, , of an object is the ratio of the surface area of a sphere with the same volume to the object's surface area: = where is volume of the object and is the surface area.