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Question Number 41726 by Necxx last updated on 11/Aug/18

Tank T_1  and T_2  initially contains  100gal of water each.In T_1  the  water is pure,whereas 150lb of  fertilizer are dissolved in T_2 .By  circulating liquid at a rate of  1gal/min and stirring the amount  of fertilizer y_1 (t) in T_1  and y_2 (t)  in T_2  change with time t.  a)with a schematic diagram write  the model linear equations for  the mixing problem.  (b)determine the eigenvalues and⊛  and eigenvectors of the derived  equation.

$${Tank}\:{T}_{\mathrm{1}} \:{and}\:{T}_{\mathrm{2}} \:{initially}\:{contains} \\ $$$$\mathrm{100}{gal}\:{of}\:{water}\:{each}.{In}\:{T}_{\mathrm{1}} \:{the} \\ $$$${water}\:{is}\:{pure},{whereas}\:\mathrm{150}{lb}\:{of} \\ $$$${fertilizer}\:{are}\:{dissolved}\:{in}\:{T}_{\mathrm{2}} .{By} \\ $$$${circulating}\:{liquid}\:{at}\:{a}\:{rate}\:{of} \\ $$$$\mathrm{1}{gal}/{min}\:{and}\:{stirring}\:{the}\:{amount} \\ $$$${of}\:{fertilizer}\:{y}_{\mathrm{1}} \left({t}\right)\:{in}\:{T}_{\mathrm{1}} \:{and}\:{y}_{\mathrm{2}} \left({t}\right) \\ $$$${in}\:{T}_{\mathrm{2}} \:{change}\:{with}\:{time}\:{t}. \\ $$$$\left.{a}\right){with}\:{a}\:{schematic}\:{diagram}\:{write} \\ $$$${the}\:{model}\:{linear}\:{equations}\:{for} \\ $$$${the}\:{mixing}\:{problem}. \\ $$$$\left({b}\right){determine}\:{the}\:{eigenvalues}\:{and}\circledast \\ $$$${and}\:{eigenvectors}\:{of}\:{the}\:{derived} \\ $$$${equation}. \\ $$

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