Question: A tubular centrifuge bowl is to separate chlorobenzene, with a density of 1109 kg/m3, from an aqueous wash liquid having a density of 1020 kg/m3. The tubular bowl having an inside diameter of 150 mm, is rotating at 8000 r/min. The free-liquid surface inside the bowl is 40 mm from the axis of rotation. If the centrifuge bowl is to contain equal volumes of the two liquids, what should be the radial distance from the rotational axis to the top of the overflow dam for the heavy liquid?

Question: A horizontal cylindrical continuous decanter is used to separate 9.93 m3/h of a liquid petroleum fraction from an equal volume of wash acid. The oil is the continuous phase and has a viscosity of 1.1 cP and a density of 865 kg/m3. The density of the acid is 1153 kg/m3. Calculate the size of the vessel (the vessel should be 95% full and the length of the tank should be 5 times its diameter).

Give me a full calculation of how to get final answers for these two questions. If you can, give me the diagram with some explanation based on theories and formulae.​