Emptying tank at 120 psi

[spoolguy]

I need some help figuring out what size valve I will need to empty an 82.34 cu. in. tank of air at 120 psi in .45 sec. I can take formula for the relationship between pressure, volume and flow rate and size the valve myself, hopefully.

Thank you for your assistance.

 

[TD2K]

This has been discussed several times but I can't seem to locate the threads. So, in that case .....

What I've done is set up a spreadsheet to do this and used the formulas out of Crane for the flow through the valve and piping (if you don't have Crane, get it, it's a great reference to have). Calculate the starting mass of air in the tank given its volume, pressure and temperature. Calculate the flow through the valve and piping for a certain period of time. You want to remove enough air that the inlet pressure changes slightly so you can assume the flow is constant over that time period. Then, calculate how much air is remaining in the tank and recalculate the pressure (you won't need to worry about temperature cooling or compressibility at these pressures). Then, redo the calculation for the next time period and repeat which is why I like a spreadsheet for this.

For inputs, you change change the valve's Cv or the time step as needed to get the solution you need. That's why I like a spreadsheet, if you need to do a smaller time step to avoid big changes in the tank pressure after each 'blow', it's trival to add more rows.

Depending how low of a tank pressure you are going, you may need at some point to switch from chocked flow through your depressuring line (where the flow rate is proportional only to the inlet pressure) to non chocked flow where the flow is proportional to the dP^2.

Fisher valves also have a depressuring calculation which I've found matches the above method pretty good, you could contact them.

 

[SooCS]

use this eq

t = 303*V/(Cv*Cf*Z*R)*((M/T)^(1/2)*ln(Pi/Pf)

t blowdown time, sec
V system inventory, ft3
Cv valve coefficient
cf critical flow factor
z compressibility
R gas constant= 10.73
T temp R
Pi initial pressure
Pf final pressure

 

[TD2K]

What's the critical flow factor? I assume M is molecular weight, is that right?

Does this assume choked flow through the valve during the depressurization?

 

[spoolguy]

I have some more questions. What would cf, z and M be for air? I assume the pressures are absolutes as well.

Of course, our Salesman had the question backward from the start. The customer was actually looking to fill the tank not empty it. Is this equation appropriate for that case as well?

Thank you for you help.

 

[TD2K]

Sales, you've gotta love them

Details, we don't need to know no stinking details!

 

[ccfowler]

TD2K,

Your summary comment is most appropriate! I fully agree!

 

[SooCS]

The equation assumed choke flow and cannot be applied for filling, which will depend on the air supply. Since this is for sales, I can derive an equation for you for filling for a fee.