# A Leaky Bathtub - competing rates & equilibrium

- Author:
- Judah L Schwartz

If water comes into a leaky bathtub at a constant rate
and leaks out a a rate proportional to the height of the
water in the tub, then an equilibrium depth of water in the tub
can be reached.
This applet can be used to explore how the equilibrium depth depends
on the rate of flow into and the rate of flow out of the tub.
Clearly, the leaky bathtub is a metaphor for many equilibrium situations
that arise because of competing rates. A height of a helium balloon to which is tied a very long string is another example. Why? Can you think of other examples?
The applet chooses a random initial volume of water. You can then watch an animation by clicking on the "play" icon in the lower left hand corner of either window.

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