I am in an attempt to calculate the time required for the smell of a bottle of perfume to reach a person's nose $10$m away. Real life experience tells me that it takes several seconds. I tried to work out this time theoretically in two different ways, but none of them gives me the right amount of time.
- I tried to find the average speed of air particles, but in room temperature, this is something near $300$ $m/s$. Clearly, this cannot be used to calculate the time taken by the perfume molecules to travel a certain distance. Their apparent speed is much slower, in that collision and the random walk takes place.
- So I tried to use the random walk formula here instead: $\langle r^2\rangle=6Dt$. But from my calculation, it takes the particles more than half a year to travel 5 meters!
I know why both method 1 and 2 are problematic. Air is not static. It is flowing all the time. I believe that it is the air's flow that allows the particles to travel 5 meters in just a few seconds. But I struggle to find a formula and a theory to explain this kind of random flow of gas. Can anyone give a model for this?