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Math Help - Two Interconnected Tanks of Mixture

  1. #1
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    Question Two Interconnected Tanks of Mixture

    Consider the two interconnected tanks as shown below. Tank 1 initially contains 30 gal of water and 55 oz of salt and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 1 gal/min (from outside). The mixture drains from Tank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min, while the remainder leaves the system. Let us denote by
    Q (t) and Q2(t) the amount of salt in Tank 1 and Tank 2, respectively.

    how to
    Formulate a system of differential equations for
    Q1(t) and Q2(t) and initial conditions that describes this flow process.

    i know how to solve this, but don't know how to set it up equation of Q1, Q2..

    Attached Thumbnails Attached Thumbnails Two Interconnected Tanks of Mixture-figureoftank1-2.jpg  
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by DMDil View Post
    Consider the two interconnected tanks as shown below. Tank 1 initially contains 30 gal of water and 55 oz of salt and Tank 2 initially contains 20 gal of water and 26 oz of salt. Water containing 1 oz/gal of salt flows into Tank 1 at a rate of 1.5 gal/min. The mixture flows from Tank 1 to Tank 2 at a rate of 3 gal/min. Water containing 3 oz/gal of salt also flows into Tank 2 at a rate of 1 gal/min (from outside). The mixture drains from Tank 2 at a rate of 4 gal/min, of which some flows back into Tank 1 at a rate of 1.5 gal/min, while the remainder leaves the system. Let us denote by


    Q (t) and Q2(t) the amount of salt in Tank 1 and Tank 2, respectively.


    how to


    Formulate a system of differential equations for
    Q1(t) and Q2(t) and initial conditions that describes this flow process.


    i know how to solve this, but don't know how to set it up equation of Q1, Q2..

    I will do the equation for Q_1 and leave the other for you. For tank 1

    Inflow: 1.5 +\frac{1.5}{20}Q_2(t) oz/min

    Outflow: \frac{3}{30}Q_1(t) oz/min

    So using minutes as units of time we have:

    <br />
\frac{dQ_1}{dt}=1.5 +\frac{1.5}{20}Q_2(t)-\frac{3}{30}Q_1(t)

    CB
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