2. pure water and salt granules are continuously fed into a well-mixed tank at a rate qw(t) [L/s] and w(t) [g/s], respectively, to produce saline solution. let c(t) [g salt/L solution] be the concentration of salt in the saline solution in the well-mixed tank and qout (t) [L/s] be the volumetric flow rate of saline solution out of the tank. in contrast to the lecture notes, here qw # qout. to relate qw to qout, we model the density p [g/L] of the saline solution as a function of the salt content, via p(c) = Pw+acwhere pw [g/L] is the density of pure water and a [g/g] is a constant identified from experimental data as in the plot below. Salt solids w gls water conveyor saline water density qw LIs model 1200 . expertnental data 1150 1100 p=p{c}=Pw+ ac a = 0.64 g solution/g salt 1050 saline solution Jouot LIS C g/L 1000- 0.2 salt concentration, c [g salt/L solution] 0.0 0.1 0.3 (a) (b) Figure 2: (a) our familiar saline solution process except qw 7 qout. the volume V of liquid in the tank is constant because of the overflow line. (b) density of saline solution versus concentration of salt. the line shows the model p(c) = pw+ac. your goal is to derive a dynamic model for c = c(t) in terms of the two inputs qw and w = w(t). qw(t) (a) write a component mass balance on the salt. it will be a differential equation. density of solution, p [g solution/L solution]

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