Concentration factor and rejection

Derive an equation relating yield to the concentration factor and the rejection Y=VicV.cowhereFeed TankVi = final volume on feed sidePermeateV, cMembraneQp , cp= final concentration on feed sideCartridgeV. = initial volume on feed sidec. = initial concentration in tankAlso transform the equation for yield to the equation in the notes which gives thefinal concentration as a function of the initial concentration, the concentration factorand the rejection, i.e.,Cf= CoCFPumpHint:In the batch system shown, the symbols are defined as_Qp= rate of permeate flow at time tSet up a differential equation relating the permeate flow rate, Qp, to the rate ofvolume change on the feed side. Set up another differential equation relating theamount of solute in the permeate to the change in the amount of solute on the feedOV = volume in feed side of system at time tside of the system.Cp =concentration of solute in the permeate at time t= concentration in the feed side of system at time tNote that the recirculation rate is very high compared to the permeate rate.Remember that the rejection coefficient is defined asO = 1 – Cp /cFor this process derive an equation relating the yield to the concentration factor andthe rejection, i.e.Y = f(CF,0)where the yield, Y, is defined as

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