Solve the following problems neatly and systematically. Use free-floating decimals in all your calculations and express your answers in 4 decimal places.

Please answer 1,2,3

1. Derive a formula to calculate for the height, Zc of the heavier liquid overflow leg in a continuous vertical cylindrical decanter. The pressure at the discharge point of the heavier liquid is given as 90% of the pressure on top of the fluid mixture. Express the height of the heavier liquid as Zx and the height of the lighter liquid as Z. Denote for "A" as the lighter liquid and "B" for the heavier liquid. (Note: Pressure of the vapor is not equal to atmospheric pressure). 2. With the formula derived and the conditions applied in problem statement #1, calculate for the heavier liquid overflow leg, the diameter, and the volume of the tank in separating liquid B from liquid A having densities of 1278 kg/m' and 794 kg.m", respectively. The volumetric flowrate of the mixture entering the tank is 30 m/hr and the viscosity of the lighter liquid (continuous phase) is the same as the viscosity of water @ 35C. Volume of heavier liquid is twice the volume of the lighter liquid and having a tank diameter to height as 1:2 ratio. Assume for 10% from the tank volume allotted for the vapor space having a pressure of 50 kPa. 3. If the liquids in problem statement #2 are to be separated in a tubular centrifugal bowl having an inside diameter of 200 mm rotating at 12,000 rpm with a free liquid surface of 55 mm from rotational axis, what should be the radial distance, from the rotational axis to the top of the overflow dam of the heavy liquid