The diameter of a spherical steel particle settling in an oil can be calculated using Stokes’ Law. Stokes’ Law is a mathematical equation that expresses the drag force resisting the fall of small spherical particles through a fluid medium1. According to Stokes’ Law, the terminal velocity v of a spherical particle falling through a fluid is given by v = (2/9) * (d1 - d2) * g * r^2 / η, where d1 is the density of the sphere, d2 is the density of the fluid, g is the acceleration due to gravity, r is the radius of the sphere and η is the viscosity of the fluid1.
In your case, you have provided the terminal velocity v = 55 mm/s, the density of oil d2 = 820 kg/m3, the density of steel d1 = 7870 kg/m3, and the viscosity of oil η = 10 mN.s/m2. By substituting these values into the equation for terminal velocity and solving for r, we can find that the radius of the steel particle is approximately 0.002 m. Therefore, its diameter would be approximately 0.004 m or 4 mm.