**Residence Time**

This is a good opportunity to discuss the notion of a residence
time for a reservoir. The residence time is effectively the average
length of time that an entity, in this case a water molecule, will
remain in a reservoir. It is really only meaningful for a reservoir
that is at or near a steady state condition. By definition, the
residence time is the amount of material in the reservoir, divided by
either the inflow or the outflow (they are equal when the reservoir
is at equilibrium). If there are multiple inflows or outflows, then
we use the sum of the outflows or inflows to determine the residence
time. For our bathtub system here, the residence time is thus 10
liters divided by 1 liter per second, which is equal to 10 seconds.
It is fairly easy to see that if we increase the flow rates, the
water moves through the reservoir faster, so the residence time
decreases. In the form of an equation, this definition is expressed
as:

It is possible then, to determine any of the above three
parameters if the other two are known and if we assume the system is
in a steady state. For instance, if we assume that the human
population is in a steady state (of course it is not), and if we know
the average lifespan, we can calculate the number of births and
deaths in a year. The population is 5.6 billion, so if we assume an
average lifespan of 70 years, then we can say that 80 million people
are born each year and 80 million people die each year, assuming a
steady state.

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