A bicycle tire that has a slow leak,

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Homework Statement


If you poke a hole in a container full of gas, the gas will start leaking out. In this problem you will make a rough estimate of the rate at which gas escapes through a hole.

Your bicycle tire has a slow leak, so that it goes flat within about an hour after being inflate. Rougly how big is the hole? (use any reasonable estimate for the volume of the tire.)


Homework Equations



N(t)=N(0)exp(-t/tau), tau being the characteristic time.
dN/dt=-A/2V*sqrt(kT/m)*N

The Attempt at a Solution



By rouglhly how big is the hole, do they want me to guesstimate the volume of the tire?
 
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Did anyone not understand my question or solution?
 
I did not. It's not clear to me what is meant by the tire becoming flat. V=0?
In this case, volume should be a variable. Which should mean that you can't integrate the second equation and get the first one. So they contradict each other. Can you tell me how the second equation is derived? That is, what is the situation for which it holds?
 

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