How Long Does It Take for Compressed Air to Deplete from a Tank?

[sambyrd220390]

I have a storage tank of 40 litres with compressed air, compressed to 9 bar (absolute), which is then fed through 8mm diameter pipe to a motor. The final pressure of the air is atmospheric (1 bar). The system is run until the storage container is depleted. Is there an equation that can find the time to take until the air runs out? Also i would like to plot this as a function of time, is there an equation to do this? I am assuming that temperature is constant.

 

[mfb]

Is there some valve to reduce the pressure? The motor could block the air flow somehow.

There are ways to calculate this, but I'm not sure how the setup looks like.
How long is your pipe?

The temperature of the expanded air will be below room temperature.

 

[Chestermiller]

I have a storage tank of 40 litres with compressed air, compressed to 9 bar (absolute), which is then fed through 8mm diameter pipe to a motor. The final pressure of the air is atmospheric (1 bar). The system is run until the storage container is depleted. Is there an equation that can find the time to take until the air runs out? Also i would like to plot this as a function of time, is there an equation to do this? I am assuming that temperature is constant.

You need to determine the pressure drop-flow rate relationship for the pipe. If there is a valve, you need to determine the pressure drop-flow rate relationship for the valve. You then do a mass balance on the tank, and couple this with the ideal gas law and the pressure drop-flow rate relationships. This allows you to solve for the pressure in the tank as a function of time.

Chet