Problem 1 A 100 gal tank contains 10 lb of water. The tank is ?lled by two inlet streams, one of pure water and one of pure ethanol. The ?ow rate of both streams is 10 gal/min. find out the concentration of ethanol (in weight % and in g/cm^{3}) when the tank is full.
Additional data: The density of ethanol/water solutions is given by the empirical equation
ρ = a_{0 }+ a_{1}W + a_{2}W^{2}
Where ρ is the specific gravity at 20 oC referenced to water at 4 oC, W is the weight percent of ethanol in the solution (0–100) and a_{0} = D 0:99669; a_{1} = 0:0012405; a_{2}= - 8:3609 * 10^{-6}
Problem 2: A tank contains 50 gal of a solution of NaCl in water (20% wt). To wash the tank, we supply fresh water at 10 gal/min and drain the tank at the constant rate of 10 gal/min. Determine the concentration of salt in the tank as a function of time and the time till the tank is free of salt. The density of solution may be assumed independent of salt concentration and equal to that of water.
Problem 3 (Bonus Problem) A tank contains 50 gal of a solution of NaCl in water (20% wt). To wash the tank, we supply fresh water at 10 gal/min and drain the tank at the constant rate of 10 gal/min. Determine the concentration of salt in the tank as a function of time and the time till the tank is free of salt. The density of NaCl solutions is given by the empirical equation
ρ = ρ_{0} + 0:925w
where ρ is the solution density (g=cm^{3}), 0 is the density of fresh water (1 g=cm^{3}) and w is the mass fraction of NaCl. (Hint: Requires numerical integration.)