Question

In a decontamination plant, we have the following tank system:


Tank A: Vo= 100 liters, concentration at the inlet Co = 2 gr / liter qo = 1000g (initial quantity of pollutant in tank A) Inlet flow rate = 3 liters / second = outlet flow rate Tank B: Tank A Vo = 100 liters qo (O) = 0g (initial quantity of pollutant in tank B) Outlet flow rate = 3 liters / second Pure water is added at a rate of 1 liter / s 7 Tank B


a) Write the differential equation allowing to model the quantity of pollutant in the tank A and solve this differential equation.

b) Write the differential equation allowing to model the variation of the volume in the tank B.

c) Write the differential equation allowing to model the quantity of pollutant in the tank B and solve this differential equation.

d) When does the volume of tank B reach 200 liters? Calculate the quantity of pollutant in tank A and B when tank B reaches 200 liters.

Answer 1

let at time t HA (t) be the amount of sand polluted in trik (A) and ablt) be amount of pollutant in twok (B) where tlinsecond) a) dua dot no=1000g 2x3 -3RA 100 daA = 6 - 30A dt loo dala +3NA = 6 dt 100 els rost = 16 let Jo estedt te HA HA 200+ cé Bot HA(0) = 1000 = 200+ c (=800 (ingrum) HAt) = 200+800 é b ) let v (t) be volume in tonk B at time t Cinsecond) V(0)=100 lite dv at (3+1) -3 dv It V (t)=tto V(o)=100=0 v (t) = 10ott litre

so 101 da B 3 NA 3 dB Toott AB (O) = 0 dt loo 3 t I OD d AB dt +34B = 6+24 e 2 loott + 3 Toott HB e =/(6 + 24 tot en 16 +24 ét) (troo}dt+G HB (t+100) c) 800 (94-36 of 75100oot +26000 HB (t+100)3 = 3 (ttoo) 9 2 + 2 + 800 (26000000) 9 (100)3 (70013 AB(0) = 0 = 3 (100) 2 + c =0 300 2 8 (26) g (1003 (1003 208-300 -1142 G= ~1142 (1003 9 ag(t)= 3 (t+100) - 800 (9 t + 3600 t² + 5loooot +26000) 34 g (hou? - 1142 (1008 9 (t+100) d) V (t) = loott a 200 t=100 second SO

XA (100) = 2out 8oo e Cin grum) A Rhodos