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The equivalent spherical diameter of an irregularly shaped object is the diameter of a sphere of equivalent geometric, optical, electrical, aerodynamic or hydrodynamic behavior to that of the particle under investigation. [1] [2] [3]
In applied sciences, the equivalent radius (or mean radius) is the radius of a circle or sphere with the same perimeter, area, or volume of a non-circular or non-spherical object. The equivalent diameter (or mean diameter ) ( D {\displaystyle D} ) is twice the equivalent radius.
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 ...
where r is the radius and d is the diameter of the sphere. Archimedes first derived this formula by showing that the volume inside a sphere is twice the volume between the sphere and the circumscribed cylinder of that sphere (having the height and diameter equal to the diameter of the sphere). [6]
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),
This enables rapid measurement of a particle size distribution by an instrument, but does require some form of calibration or assumptions regarding the nature of the particles. Most often this includes the assumption of spherical particles, thus giving a result which is an equivalent spherical diameter. Thus, it is usual for measured particle ...
Spherical coordinates (r, θ, φ) as commonly used: (ISO 80000-2:2019): radial distance r (slant distance to origin), polar angle θ (angle with respect to positive polar axis), and azimuthal angle φ (angle of rotation from the initial meridian plane). This is the convention followed in this article.