Sphericity is a measure of the roundness of a shape. A sphere is the most compact solid, so the more compact an object is, the more closely it resembles a sphere. Sphericity is a ratio and therefore a dimensionless number. It has applications in geology, where it is important to classify particles according to their shape. Sphericity may be calculated for any three-dimensional object if its surface area and volume are known.
Instructions 3V/4π = r^3 => r = (3V/4π)^(1/3).
3. Express the surface area of the sphere in terms of its volume. The surface area of a sphere is A = 4π r^2. Using the solution for r obtained in Step 2, we have A = 4π (3V/4π)^(1/3)^2 = 4π (3V/4π)^(2/3) = 4π^(1/3)(3V/4)^(2/3) = π^(1/3)(4^(3/2)3V/4)^(2/3) = π^(1/3)(8)3V/4)^(2/3) = π^(1/3)(6V)^(2/3). Therefore, A = π^(1/3)(6V)^(2/3) for all spheres.
4. Substitute the equality A = π^(1/3)(6V)^(2/3) obtained in Step 3 into the equation Y = As/Ap for the sphericity given in Step 1. This gives us Y = As/Ap = π^(1/3)(6V)^(2/3)/Ap. Thus, the sphericity of a particle P is given by Y = π^(1/3)(6Vp)^(2/3)/Ap, where Vp is the particle's volume and Ap is its surface area.
5. Interpret the sphericity ratio. Since a sphere is the most compact three-dimensional object, As <= Ap so 0 < Y <= 1. Thus, the closer the sphericity is to 1, the more round P is.
Tags: surface area, area sphere, most compact, obtained Step, sphere most
