- #1
Adel Makram
- 635
- 15
Homework Statement
Suppose there is solute ##s## in a bowel containing fluid. There is a tiny hole near the bottom which leaks a small fixed volume of solute ##\lambda## per unit time ##dt##. In addition, there is a small added solute to the fluid in a constant rate ##\alpha## so as the volume of the fluid is constant.
What is the equation of ##s## at any ##t##?
Homework Equations
The Attempt at a Solution
If there is no added solute, the equation of ##s## should be ##s=s_0 e^{-\lambda t}## where ##s_0## is the initial amount of the solute at ##t_0##.
Now, I tried to include the added solute as linear function of ##t##.
##ds=(-\lambda s+\alpha)dt##. If ##\alpha=0##, we get the equation above. But I do not know how to get ##s## if ##\alpha## is not zero. Or may be, ##s## can be obtained from different approach!