Question

TANKA TANKB Figure 1 Figure 1 shows a mixture problem having 2 tanks of Tank A and Tank B. Suppose x(t) and y(t) represent the amount of salt in tank A and tank B respectively in which the two tanks are connected to each other. Tank A contains 800 liters of water initially containing 20 grams of salt dissolved in it and tank B contains 1000 liters of water and initially has 80 grams of salt dissolved in it. Salt water with a concentration of gram/liter of salt enters tank A at a rate of 4 liters/hour. Fresh water enters tank B at a rate of 7 liters/hour. Through one connecting pipe water flows from tank B into tank A at a rate of 10 liters/hour. Through a different connecting pipe 14 liters/hour flows out of tank A and 11 liters/hour are drained out of the pipe (and hence out of the system completely) and only 3 liters/hour flows back into tank B. a) Label Figure 1 with the given information to represent the mixture problem. (3 marks) b) Construct a system of differential equations that describe the amount of salt in tank A and tank B at any time t. (7 marks)

Answer 1

salt 1/2 916 @ 4 isht hatiny Freshwater @ allar (a) Tank B Tank A lolno 800 euater 1000 l weeter salt=20g scelts 80g 14 Chr 341 WW (6) At time it x St), y(A) represent represent salt in tank A, tam B. (9,918, 44fdro) So, (0gm)2, I tho ten of 1000 gle, 100/hr tankB 1000 l, y(t) 8ool wat Salt aut) 31/07 276 goo gld, 144 Concentration at time ofa ylt) Grantrenon atto (t) 400 Tooo Cangle in concentration with respect to time of any time is given rate out by rate in - Vate - Concentration & flow (velocity) Soi 14 xlt) dact) dt 1 x4 et YIt) 1000 * 10 olx 2 - 2 + y .R et 100 3 49) + d yet) alt 02. 10x ) goo Tooo dy dt 3 x goo y 100 so 19 -7 400 + +2 da alt dy at 3 - bo 100 g Answer