I have a project which I am working on which is trying to work out the Potential Energy from a Vessel filled with compressed air. I have found a few different equations for this and was wondering if anyone has any experience on this to guide me a little.

To first size the receiver I have used the equation

\( Vh = \frac{t \times (q_s \times p_a)}{P_1-P_0}\)

Where

\( Vh \) = volume of the receiver tank (cu ft)

\( t \) = time for the receiver to go from upper to lower pressure limits (min)

\(q_s \) = free air flow (scfm)

\( p_a\) = atmospheric pressure (14.7 psia)

\( P_1 \) =maximum tank pressure (psia)

\( P_0 \) = minimum tank pressure (psia)

And now I used the following equation to find the stored energy

\( U = \frac{P_h \times V_h}{\gamma-1}\times (1-(\frac{P_1}{P_h})^{\frac{\gamma-1}{\gamma}})\)

Where

\( U \) = Stored Energy

\(P_h \) = The absolute pressure of the vessel.

\(V_h \) = The volume of the vessel

\(\gamma\) = The adiabatic exponent or ratio of specific heats,1.4 for diatomic gases such as Air

\( P_1 \) =The absolute pressure to which the vessel would drop if it burst

Are these equations correct for the tasks which I am trying to work out?

Now there is two other parts which I would like to find but having trouble finding the correct information

1. The compressor size and CFMs required

2. How to calculate the output CFM though different diameter pipe if the vessel was to be released

Have I been using the correct formulas for the sizing and potential energy and could anyone help me with the Compressor sizing and CFM though different diameter pipe work.

Thanks for your help

Kayne