Mixing Problem in Tank using Differential Equations
3 years ago
19
Here is the problem statement:
"A tank initially contains 10 𝑘𝑔 "of salt in" 100 𝐿𝑖𝑡𝑒𝑟𝑠 of water. The contents of the tank flow out at a rate of 10 𝐿𝑖𝑡𝑒𝑟𝑠∕𝑚𝑖𝑛. Salt water with a
concentration of 0.01 𝑘𝑔∕𝐿𝑖𝑡𝑒𝑟 flows into the tank at a rate of 10 𝐿𝑖𝑡𝑒𝑟𝑠∕𝑚𝑖𝑛. How much salt is in the tank after 11 minutes?"
The problem is solved by examining the big picture, finding the governing differential equation, finding the general solution with the method of separable equations, finding the particular solution, solving for the question, and finally plotting the slope and solution and finding the equillibrium solution.
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