Question

(a) A 10L tank is filled with a mixture having an initial concentration of 4 g/L. An inflow pipe pumps in a mixture at a rate of 2L/min with a variable concentration of 2t g/L (i.e. the concentration is increasing with time). If the outflow pump is set to 3L/min how much mass of chemical remains when the tank is half fll (or half-empty if you'd rather look at it that way) (b) What should we set the initial concentration of the tank to be if we hope for the concentration to stay the same the moment the tank is half full? (i.e. instead of the the 4g/L in the previous part, what should we replace this value with)

Answer 1

VCo)=loL Jlol= /0xy nbon 2 x2t, 4t Rin 34 X3 Rout vto)+(2-3t 10-t Rin-Rout 4t- 3y 1o-t at dy 434 Yt dt to- t NoLo Solre kes oDE dyPyso P- 3 10-t dt l0-t -3&|0-t e = e penal Solution x ytdt 10-2 tdlt TTo-g3 (0-t)3 +5 (o-t) t l0-t) (0- t)3 te10-4 y4--t5 (lo-t) 0-teu tc Clo-t)3 -dlt du a -4 (l0-t)+20 ( L0-t) + c Clo-t)3 o du Put lted y-40)+2oxjotCl0) 4D du looo C240 C o 24 -4 (10-t)20 (10 -t) + o.24 (10-t) utlou3H Half ful t_5 when 3-2 5)= -4(/0-5)20 ( 10 -5) 0 2 30 9m