The purging of stirred tank systems

In industry it is common practice to use a number of tanks equipped with agitators in series. Frequently it is necessary to know the time required to reduce the concentration of off-quality material in the system below a certain acceptable limit. 

Let a mass m of solute be dissolved in a liquid volume V in the first stirred tank, there being no solute in the other tanks. Let solute free liquid flow into the tank at a volumetric flow rate Q. Let liquid flow from the tank at a volumetric flow rate Q. If the liquid in the tank is uniformly mixed the discharge liquid contains a concentration of solute m/V which is the same as the solute concentration in the tank. 

The rate of change of the mass of solute in the tank is given by the equation 

The fraction x of the original solute which has been purged from the tank after a time t is given by the equation 

---