# Potential Energy in a Vessel

#### Kayne

Joined Mar 19, 2009
105
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.

Kayne

#### #12

Joined Nov 30, 2010
18,224
I think you're on the wrong website. You might get lucky and have an answer here, but most integrated chips do not use compressed gasses.

Maybe the Physics forum on this site...I'll ask the moderators.

#### Kayne

Joined Mar 19, 2009
105
OK, I see you point, it was a gamble which may not pay off.

I am more interesed in working out the energy so that I can then use this to power a generator like a Compressed Air Energy System.

I have added it into the Physic forum now also.

Thanks

#### WBahn

Joined Mar 31, 2012
30,088
I'm surprised that the potential energy calculations don't include the absolute temperature somewhere.

If you are wanting to use the stored energy for something like a turbine (or anything, really) you will need to take into account the loss of energy as it exits the tank into the connecting plumbing. This is a throttling process and is how you drop the energy in the gas stream coming out of the condenser coils in a refrigerator.

Your compressor ratings will need to reflect some of the operating conditions, as well. I think the formulas you have are for quasi-static processes that are isothermal. But in the real world if you put your hand on the output pipe of a compressor you will immediately appreciate that this process is anything but isothermal. So a considerable portion of the energy put into the air stream by the pump will get lost as heat and only some of it will end up in the potential energy of the compressed gas in the tank once it has cooled down to ambient temperature.

Decent approximations for these various processes are the realm of "engineering thermodynamics" and there are several different energy definitions, such as Gibbs Free Energy and Helmholtz Free Energy, that deal with them. So find an introductory text or website on engineering thermo. Do NOT look into physics texts, which are principally statistical thermodynamics and, while extremely fascinating and illuminating, are very difficult to apply to engineering situations directly.