I need to generate a graph showing the pressure of a tank vs. time. I will have a large tank pressurized, with air, at P1 connected to a smaller tank with piping of a known area A. The larger tank will be much larger than the smaller tank, therefore, we can assume the large tank will stay at P1. The smaller tank has a volume of Vt

This question is almost identical to this question from the past from Cheresources: http://www.cheresources.com/invision/to ... elstorage/

However, I do not feel like the question was fully answered in that post. The equation that the poster was working with is:

ρair*v*A = [Vt*MWair/(ZRT)]*d(P-P1)/dt

Like the original poster, I am confused on how to calculate the velocity (v) and I understand that it changes as the pressure differential between the two tanks changes.

Additional Assumptions: No temperature change, friction from tubing is negligible.

Thanks so much in advance!

## Calculating Pressure Vs. Time While Filling Tank

### Re: Calculating Pressure Vs. Time While Filling Tank

You can look at post here:

viewtopic.php?f=3&t=10

This is similar problem as yours, but not exactly the same.

Your equation is I think correct but have to clarify some abbrevations used:

Vt - is volume of tank

MWair what is for?

rho * V * A = G = dm/dt is mass flow rate kg/s.

Ideal gas equation is pV = mRT => m = pV / RT; dm/dt = G = d/dt(pV/RT). For V=const, R=const. T=const. it is

dm/dt = rho * V * A = G = V/RT dp/dt.

The problem is that mass flow rate G is changing over time due to pressure drop. You have to use another equation for it and for your problem I think that you should use one of these two equations:

http://www.pipeflowcalculations.com/pip ... -and-pipes.

As you can see flow rate is depending on expansion factor, internal pipe diameter, resistance coefficient, and density at the start:

G = 1.111x10^-6 * Y * d^2 * ((p-p1)*rho1/K)^2.

This all leads to rather complex solution but as far as I can tell it will give result. Looking for comments on this as I would like to get the solution for this problem and develop calculator for problems like this.

Final diagram will look like the function t = K(p-p1)ln(p-p1) but exact calculation for K needs to be done.

viewtopic.php?f=3&t=10

This is similar problem as yours, but not exactly the same.

Your equation is I think correct but have to clarify some abbrevations used:

Vt - is volume of tank

MWair what is for?

rho * V * A = G = dm/dt is mass flow rate kg/s.

Ideal gas equation is pV = mRT => m = pV / RT; dm/dt = G = d/dt(pV/RT). For V=const, R=const. T=const. it is

dm/dt = rho * V * A = G = V/RT dp/dt.

The problem is that mass flow rate G is changing over time due to pressure drop. You have to use another equation for it and for your problem I think that you should use one of these two equations:

http://www.pipeflowcalculations.com/pip ... -and-pipes.

As you can see flow rate is depending on expansion factor, internal pipe diameter, resistance coefficient, and density at the start:

G = 1.111x10^-6 * Y * d^2 * ((p-p1)*rho1/K)^2.

This all leads to rather complex solution but as far as I can tell it will give result. Looking for comments on this as I would like to get the solution for this problem and develop calculator for problems like this.

Final diagram will look like the function t = K(p-p1)ln(p-p1) but exact calculation for K needs to be done.

Pipe flow calculations - since 2000

### Re: Calculating Pressure Vs. Time While Filling Tank

MWair is the molecular weight of air.