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 x(t) [g salt/g solution] be the mass fraction of salt in the saline solution in the tank. Let q(t) [L/s] be the volumetric flow rate of saline solution out of the tank. In contrast to the lecture notes, note that qwq. To relate q to qw, we model the density p [g/L] of the saline solution as a function of the salt content, via p(x) = Pw + ax where pw [g/L] is the density of pure water and a is a constant identified from experimental data as in the plot below. water 9. L/s salt granules w g/s V.x salty water 9 L/s xg salt/g solution density of solution, p [g/L] saline water density 1200 nodel experimental data 1150- 1100- 1050 (a) 1000- 0.00 0.05 0.10 0.15 0.20 mass fraction NaCl, x (b) 0.25 Figure 2: (a) our familiar saline solution process except qwq. the volume V is constant because of the overflow line. (b) density of saline solution versus mass fraction of salt. the line shows the model p(x) = Pw + ax. = Using p(x)=pwax, derive a dynamic model for the mass fraction of salt, x = x(t), with qwqw(t) and w= w(t) as model inputs. The variable q should not appear in your dynamic model (hint: write the total mass balance to eliminate q from the salt balance). Check your units!