Model: Mixing Problem – 1 Tank
Rum and Coke solution.
1. Maintain constant tank volume.
2. Inlet and outlets supply and drain at the same rate.
3. Instantaneous & thorough mixing
How much rum is present in the tank at any time t?
We want to track the amount of rum at a given time.
More on Separable Equations
Where M and N are expressed entirely in terms of their paired derivative we are able to find …
This is an exact solution
Super position principle & Variation of Parameter
we would like to solve for . The solution to the second is called the complementary function, called . The solution to the first is where is a particular solution for equation and compensates for the input function.
where M(x) is a separable equation. Solve the homogeneous solution first then allow the form of the homogeneous equation to help you get going on the right track for the particular/non-homogeneous. Multiply by M(x) and solve for M(x). Do remember to check things out after the fact though.
Since My and Nx are not the same, we can do some fancy work to make things fun.
We can use this to solve our equation for f and find out what our integrating factor is.
Assume that Fy or Fxis 0 and solve for f=F(x) or f = F(y), respectfully.