Problem 45391. Calculate the sphericity of a Raschig ring

Sphericity is a measure of the roundness of any particle. It was defined by Wadell in 1935 as the ratio of the 'surface area of a sphere having the same volume as the given particle' to the 'surface area of the given particle'. By definition, the maximum value of sphericity is 1, which is that of a perfect sphere. The more elongated a particle is, the lesser its sphericity.

A Raschig ring is a common particle found in packed beds that are shaped like small pieces of a tube (see figure). As a hollow cylinder, it has a height H, inner radius R1, and outer radius R2. The sphericity of a Raschig ring is important to calculate as it can influence the performance of a packed bed for adsorption.

Make a function that takes three values: H, R1, and R2. Output the sphericity of this hollow cylinder rounded to 4 decimal places. You are ensured that:

• H, R1, and R2 are all positive integers
• R1 < R2
• All inputs have consistent units; and
• No input value exceeds 100.