Problem 1 (Centrifugation) (30 points) A mixture containing particles with a density of 1764 kg/m³ is to be clarified by centrifugation. The fluid density is 1065 kg/m³ and its viscosity is 1.319 cP. The centrifuge has a bowl with r2 = 50 mm, r₁ = 10 mm, and height b = 250 mm. If the critical particle diameter in the exit stream is 150 um and the mixture is fed at a flow rate of 100 L/h, at what speed should the centrifuge be operated? The centrifuge is designed to have speed increments of 5 rpm.