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(Solved): Closed Three-Tank System Problems 35 through 37 deal with the closed three-tank sys- tem of Fig. 7.3 ...
Closed Three-Tank System
Problems 35 through 37 deal with the closed three-tank sys-
tem of Fig. 7.3.5, which is described by the equations in (24).
Mixed brine flows from tank 1 into tank 2, from tank 2 into
tank 3, and from tank 3 into tank 1, all at the given flow rate r
gallons per minute. The initial amounts x_(1)(0)=x_(0) (pounds),
x_(2)(0)=0, and x_(3)(0)=0 of salt in the three tanks are given,
as are their volumes V_(1),V_(2), and V_(3) (in gallons). First solve
for the amounts of salt in the three tanks at time t, then determine the limiting amount (t->+\infty ) of salt in each tank.
Finally, construct a figure showing the graphs of x_(1)(t),x_(2)(t),
and x_(3)(t).
r=10, x_(0)=18, V_(1)=20, V_(2)^(-)=50, (V_(3))=20