Consider a primary sedimentation tank (PST) in a water treatment plant with Surface Overflow Rate (SOR) of $40\:m^3/m^2/d$. The diameter of the spherical particle which will have $90$ percent theoretical removal efficiency in this tank is ______ $\mu m$. Assume that settling velocity of the particles in water is described by Stokes’s Law.
Given: Density of water $=1000 \: kg/m^3$; Density od particle $=2650 \: kg/m^3$; $g=9.81 \: m/s^2$; Kinematic viscosity of water $(v) = 1.10 \times 10^{-6} m^2/s$.