2. Pure water and salt granules are continuously fed into a well-mixed tank at a rate q(t) [L/s] and w(t) [g/s], respectively, to produce saline solution. Let r(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 qq. 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) = p + az where p g/L] is the density of pure water and a is a constant identified from experimental data as in the plot below. water 4. L/s salt granules w.g/s 00000 8 V.c salty water q L/s x9 salt/g solution density of solution, p [9/L] 1200 1150 saline water density model experimental data 1100 1050 (a) 9.16 4.45 4.18 0.15 0.20 0.25 Pass fraction act, x (b) Figure 2: (a) our familiar saline solution process except q, q. (b) density of saline solution versus mass fraction of salt. the line shows the model p(z) = Po +αr. 1(t), Using p(z) =P + or, derive a dynamic model for the mass fraction of salt, r = with q (t) and w w(t) as model inputs. The variable q should not appear in your dynamic model (hint: balance). Check your units! write the total mass balance to eliminate q from the salt