Potential Energy in a Vessel

[Kayne]

Hi,

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

 

[Achy47]

Hello Kayne,

It looks like you are on the right track with your equations for determining the potential energy from a vessel filled with compressed air. However, it is important to note that these equations are based on certain assumptions and may not be entirely accurate in real-world scenarios. It is always recommended to consult with an expert or conduct experiments to validate your results.

As for determining the compressor size and required CFMs, this will depend on the specific application and the desired pressure and flow rates. It is important to consider factors such as the type of compressor (reciprocating, rotary, etc.), the efficiency of the compressor, and the pressure and flow requirements of the system. Consulting with a compressor manufacturer or expert in the field can help you determine the appropriate size and CFMs for your project.

Calculating the output CFM through different diameter pipes can also be complex and may require experimentation or computer simulations. The flow rate through a pipe is affected by factors such as the diameter, length, and roughness of the pipe, as well as the pressure and temperature of the air. There are various equations and tools available for calculating flow rates through pipes, but it is important to double-check your results and consider any potential errors or uncertainties.

Overall, it seems like you are making good progress on your project. I would recommend consulting with an expert or conducting further research to validate your equations and determine the appropriate compressor size and CFMs for your specific application. Good luck with your project!