The general form for the shape factor of any shape is: K s (D e A) / V where K s : Shape Factor D e : Equivalent Diameter of a sphere with a volume equal to the volume of the nonspherical particle A : Area of the shape V : Volume of the shape By setting the equation for the volume of a sphere and the volume of the shape in question (in this case a cylinder) we can find D e D e ((3/2) D 2 h) (1/3) D e : Equivalent Diameter D : Diameter of the cylinder h : height of cylinder Substituting the formula for the area and volume of a cylinder and the D e into the general form will give us the shape factor for a cylinder.
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