Determining Constant Mass Flow Rate in a Compressed Air System

[Calculost]

It's been a long time since I had to do any calculus and longer still since I had to deal with ideal gases but now I'm confronted with both.

The problem setup is this:

Air is coming into a compressor at a known mass rate, pressure and temp.

It's being compressed to fill a known tank volume at at given pressure and temperature. Once that pressure is reached the regulator allows air to leave maintaining the same pressure.

I want to plot a graph with the Flow rate vs time.

I was able to get a formula (in terms of Volume, Pressures, Temperature and time) that graphed but it didn't contain the mass flow rate. Seems to me that's important and thus the answer trailed off to almost Zero at the time to fill the tank. I know that's not right. At the moment the regulator releases air the flow rate will remain constant.

the basis is Mass Flow Rate = constant

start making substitutions, intergrating .. bla, bla, bla .. I get lost and need a beer.

Can you help an old fart out here?

 

[rcgldr]

Air is coming into a compressor at a known mass rate, pressure and temp. Once ... pressure is reached the regulator allows air to leave

Once the tank has reached the target pressure and the regulator allows the air to leave, then the mass flow out of the regulator is the same as the known mass flow rate going into the compressor (since no more air is going into the tank).

This is ignoring issues like the tank initially getting hot while being filled, then cooling off requring more air flow into the tank in order to maintain pressure while it cools off.

 

[Calculost]

Correct. It's the time from t=0 UNTIL the tank is filled that is of interest.

I've attached the work I've done so far. As I said in my initial post, since the formula I derived doesn't contain the initial mass flow rate I question it's validity.