Solving Pneumatic Equation with Natural Logarithm

[DrZygote214]

I'm trying to find a particular equation that I came across years ago, but have since forgotten, and probably never knew the name or if it even had a name.

Basically, if you have two regions with different pressures, and a hole with area A between them, how long does it take before the pressures equalize?

I believe you just need the two pressures and the hole area, not the volumes or temperatures, but I may be mistaken. We might also need certain gas constants for whatever gas.

All I can remember for certain was that this equation involved the natural logarithm. Oh well. If anyone knows it, please let me know.

thanks.

 

[Valerie Park]

The equation you are looking for is called the Hagen-Poiseuille equation. It is used to calculate the amount of time it takes for two regions with different pressures to equalize when there is a hole with area A between them. The equation is as follows: t = (A/(πη)) * ln(p1/p2) where p1 and p2 are the initial and final pressures, η is the viscosity of the fluid, and A is the area of the hole.