Question

completeness and clarity please !

Diferentia ruquations 3. Two 500 gallon tanks T, and T, intially contain 100 gallons of salt solution. A solution with 2 pounds of salt per galloon is pumped into Ty from an external source at 6 gal/min and a solution with 1 pound of salt per gallon is pumped into T, from an external source at 5 gal/min. The solution from Tis pumped into T, at 2 gal/min, and the solution from T, is pumped into Ty at 1 gal/min. Both tanks are drained at 3 gal/min. Let Q.(t) and Qu(t) be the number of pounds of salt in T, and T2, respectively, at time to (a) Draw a diagram that represents the info above. (b) Derive a system of differential equations for Q1 and Q2 that's valid until a tank is about to overflow. You may assume both mixtures are well stirred.

Answer 1

Salt spond Igal 1 pond/gal sgal/min @bgal/ min (a sri Tanlot Tamp 2 Igal/min 4 Vo = proogal No I gal/min 100 gala li 3gal/min 3 gallimin B any time t Tawe 1 Taulo 2 Volume Vo & Net flowxt = (100+ 2 t) gallon Vot 3t Salt 0.(+) Q₂ (f) Salt Concentratia 0,4) 100 f2t pond legal 040 100+34 pondigal rate in - rate out Sol Change in Concentration of Salt in galle = Rate = flow concentrations des, ai Balt) - 276 + SX 8,64) 10ot et d Q₂ (4) - SAI + 2 Bit) 4 CS2H) 100 +34 at 100 fot at 100 +2 + So dailt) = 6 S8,(1) 160+2 + 82(+) 1oort dt d Balt) at S + 2014) 100824 q G2A) 100 +34