Instructions:
DO NOT MOVE THE SLIDERS!!!
This applet proved more complicated than I thought. The animation vaguely corresponds to
when the sliders set to:
in = 3
out = 2
Cin = 2
CinT = 5
Description:
The mixing problem. Solution is dumped into a tank at a given rate(in) and given concentration(Cin).
The tank will have an initial volume (I fixed the starting volume at 100) and a starting concentration(CinT).
There is also an out flow(out). The concentration of the solution coming out is dependent on time. To find
the concentration in the tank at time t, we set up a differential equation.
dA/dt = (rate of concentration in) - (rate of concentration out)
dA/dt = r(in)*c(in) - r(out)*c(out)
For my particular example:
dA/dt = 6 - 2*A(t)/(100+t)
Using skills developed in Ordinary Differential Equations, we solve for A(t).
A(t) = 2(100+t) + C (100+t)^(-2)
My applet shows increases in the concentration of red at any given time, and shows how the concentration in general changes over time(Time).
It will also calculate the concentration in the tank for a given time(Calculation Time).
The sad truth:
My applet is very limited in what it can do. The graghics only corresponds to the original inputs.
I belive A(t) is still properly calcuated for when (out) less than (in), but fails for (out) equal to (in) or
(out) greater than (in).
With more time and proper incentive, I believe I could work out all the bugs. Thank you.
Questions:
1. What happens at time = 100?
2. How would the out flow change at time greater than 100?
3. If the tank could hold an INFINTE amount of water, how long would it take for (Cin) = (CinT)?