Question: You have been asked to design a mixing tank for salt solutions. The tank volume is 126 gal and a salt solution flows into and out of the tank at 7 gal of solutiodmin. The input salt concentration contains (3 lbm salt)/gal of solution. If the initial salt concentration in the tank is (1/2 lbm &)/gal, find:
a. The output concentration of salt as a function of time assuming that the output concentration is the same as that within the tank.
b. Plot the output salt concentration as a function of time and find the asymptotic value of the concentration m(t) as t →∞
c. Find the response time of the stirring tank, i.e., the time at which the output concentration m(t) will equal 62.3 percent of the change in the concentration from time t = 0 to time t → ∞.