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...

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Extracted text: 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+ac where 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 saline water density conveyor qw LIs model 1200- experimental data 1150 1100 - saline solution p=p(c) = pw+ ac- a = 0.64 g solution/g salt 1050 Jout LIS C g/L 1000 0.0 0.1 0.2 0.3 salt concentration, c [g salt/L solution] (a) (b) Figure 2: (a) our familiar saline solution process except qw # 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. qw(t) your goal is to derive a dynamic model for c = c(t) in terms of the two inputs qw = and w = w(t). density of solution, p Ig solution/L solution]


Extracted text: (b) write an overall (salt + water) mass balance. it will be a differential equation. (c) use the overall mass balance to eliminate qout from the salt balance, so that the input qw appears in the salt balance. also, use p(c) = Pw + ac to eliminate p from your dynamic model. write the final dynamic model as dc (.. :). dt with .. representing algebraic (not differential) expressions.