Question

(1 point) Consider two interconnected tanks as shown in the figure above. Tank 1 insal contains 100 Lters) of water and 345 g of sat, while tank 2 initally contains 90 L of water and 225 g of sait Water containing 25 gL of salt is poured into tank1 at a rate of 3.5 Lmin while the midure flowing into tank 2 contains a salt concentration of 35 gL of salt and is flouing at the rate of 2.5 Limin. The two- connecting tubes have a fow rate of 5.5 Lmin from tank 1 to tank 2 and of 2 Lmin from tank 2 back to tank 1. Tank 2 is drained at the rate of 6 Lmin. You may assume that the solutions in each tank are thoroughly mixed so that the concentration of the midure leaving any tank along any of the tubes has the same concentration of sat as the tank as a whole. (This is not completely realistic, but as in real physics, we are going to work with the approximate, rather than exact description. The 'rear equations of physics are often too complicated to even write down precisely, much less solve) How does the water in each tank change over time? Let p(t) and g(t) be the number of grams (g) of salt at time t in tanks 1 and 2 respectively. Wite differential equations for p and q (As usual, use the symbols p and q rather than p(t) and g(t).) Give the initial values |q(0) Show the equation that needs to be solved to find a constant solution to the differential equation: for all time t and q(t) A constant solution is obtained if p(t) for all time t.

Answer 1

Tanとよ Tank A LAmin 259/L /eo LWatr H hi 5-54 Sat -S L/nan Netintow nto tank 1- 3.5 2 o L/mn Net inf low to ank 25.5+2.5-2-6 I Lonentraton tan k h Lonentration in tank out f low rate rate Now intlow nto tank 1 tan k asl35)a{ S.5 Ar Swe 45

35(a.555/ /oo Ar Suten Also blo 315 235 11 Answer is obtaire A lanst ant so lution blt An swen I43 39375 3