This is a problem in batch processing of materials using a mixing tank. The mixing tank has inflow and outflow tubes and a stirrer that keeps the concentration uniform at all points in the tank. The tank is initially filled by a volume V of solution, formed by dissolving a given solute in a solvent, with concentration C0 (measured in kg/l); The inflow tube carries a solution of different concentration Cin than the initial concentration; the volumetric flowrate is Qin The outflow flowrate is Qout and, due to the well-mixed assumption, the outflow concentration has the same concentration as the instantaneous concentration of the tank. (i) Derive the differential equation governing the instantaneous concentration in the tank; (ii) Assume the tank volume is 1000 l, the volume initially contains 10 kg of salt, the rate of inflow is 2 l/s, the inflow concentration is 0.005 kg/l and that Qin = Qout (in other words, the outflow pipe carries away the overflow). Calculate and plot the instantaneous concentration of salt C(t); (iii) Calculate the time required to produce a solution of concentration 0.008 kg/l.
This is a problem in batch processing of materials using a mixing
tank. The mixing tank has inflow and outflow tubes and a stirrer that keeps the
concentration uniform at all points in the tank. The tank is initially filled by a
volume V of solution, formed by dissolving a given solute in a solvent, with concentration C0 (measured in kg/l); The inflow tube carries a solution of different
concentration Cin than the initial concentration; the volumetric flowrate is Qin
The outflow flowrate is Qout and, due to the well-mixed assumption, the outflow
concentration has the same concentration as the instantaneous concentration of
the tank. (i) Derive the differential equation governing the instantaneous concentration in the tank; (ii) Assume the tank volume is 1000 l, the volume initially
contains 10 kg of salt, the rate of inflow is 2 l/s, the inflow concentration is 0.005
kg/l and that Qin = Qout (in other words, the outflow pipe carries away the
overflow). Calculate and plot the instantaneous concentration of salt C(t); (iii)
Calculate the time required to produce a solution of concentration 0.008 kg/l.
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