# Time for a gas to expand

Gold Member
If you have a large tank of air at a certain high pressure and you open up a valve into a much smaller tank, is there a way to determine how fast the air will expand into the smaller tank?

Q_Goest
Homework Helper
Gold Member
Generally, you assume the pressure in each tank is uniform.

If you're asking how quickly air or a fluid will go from one tank to another, there are equations for determining fluid flow through valves and piping. The Crane paper #410 is the most widely used reference for those equations.

Gold Member
Dang, this cannon of ours is going to be more complex then i thougth :D

Gokul43201
Staff Emeritus
Gold Member
The rate of flow is proportional to the pressure difference across the valve and goes inversely with the impedance of the valve, which is a function of the valve length, opening size and Reynold's number of the flow (which in turn, is a function of flow velocity, and is hence determined iteratively for a general case).

Q_Goest
Homework Helper
Gold Member
Hey P, if I were going to do a really quick and dirty analysis for something like that, I'd do a spreadsheet that calculated flow through the valve only and just oversize the pipe. The valve is generally your largest restriction by far, unless you have a ball valve. If using a ball valve, just reduce it a bit. Or go through the entire system and calculate the flow at a single pressure differential, and come up with an "equivalent Cv". The Cv is the flow coefficient for the valve. If you come up with an equivalent one, it makes all the math much easier since you don't then have to recalculate flow through the pipe.