A multiunit mixing process consists of two tanks T1 and T2. Ten (10) gal/min of pure water is pumped from the outside into Tank 1 which initially contains 100 gal of water in which 120 Ib of salt are dissolved. Tank 2 initially contains 200 gal of water in which 50 Ib of salt are dissolved. Liquid is circulated continuously between the two tanks by pumping 12 gal/min from Tank 1 into Tank 2 and pumping 2 gal/min from Tank 2 into Tank 1. Also, 10 gal/min of the uniform solution in Tank 2 is taken out of the system. Thus, the volume of the content of each tank remains constant and the contents of the two tanks are kept uniform by stirring. Find the design equations that would be necessary to calculate the salt contents y1 (t) and y2 (t) in Tank T1 and Tank T2 respectively at any time t. What would be the salt contents in the tanks after a long time? When will the salt contents of the two tanks be equal and what will be the salt contents in the tanks at that time? Calculate your eigenvalues to 3D (3 decimal places). [After obtaining your quadratic equation from the determinant of (A- λI) =0 for the eigenvalues λ, you may assume the roots are λ1 = - 0.0442 and λ2 = - 0.136 for your eigenvectors].
A multiunit mixing process consists of two tanks T1 and T2. Ten (10) gal/min of pure water is pumped
from the outside into Tank 1 which initially contains 100 gal of water in which 120 Ib of salt are dissolved. Tank 2
initially contains 200 gal of water in which 50 Ib of salt are dissolved. Liquid is circulated continuously between
the two tanks by pumping 12 gal/min from Tank 1 into Tank 2 and pumping 2 gal/min from Tank 2 into Tank 1.
Also, 10 gal/min of the uniform solution in Tank 2 is taken out of the system. Thus, the volume of the content of
each tank remains constant and the contents of the two tanks are kept uniform by stirring. Find the design
equations that would be necessary to calculate the salt contents y1 (t) and y2 (t) in Tank T1 and Tank T2
respectively at any time t. What would be the salt contents in the tanks after a long time? When will the salt
contents of the two tanks be equal and what will be the salt contents in the tanks at that time? Calculate your
eigenvalues to 3D (3 decimal places). [After obtaining your quadratic equation from the determinant of (A- λI) =0
for the eigenvalues λ, you may assume the roots are λ1 = - 0.0442 and λ2 = - 0.136 for your eigenvectors].
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