# Thread: Two Interconnected Tanks of Mixture

1. ## 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..

2. Originally Posted by DMDil
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:

$
\frac{dQ_1}{dt}=1.5 +\frac{1.5}{20}Q_2(t)-\frac{3}{30}Q_1(t)$

CB