What is the Energy Produced by a 55 Gallon Barrel of Air at 500ft Depth?

[SimpleQuery]

Hi all,

This is not homework, just theory discussion with my son.
My son has been asking some interesting questions with regard to displacement as it relates to water. All kinds of teenager, “what if” stuff. I have looked around for simple formulas, but I am not embarrassed to say, I do not know how to use them. I am just a simple machinist, with simple questions.

Can some one or a couple of people help us learn to use these formulas and what formulas we should be using?

For example:
P(HP) = M(Min) HG/33000 (1)

I know what each item stands for (I think) but I need an example of the formula executed with basic numbers so I can then use it.

P(HP) = Horsepower
M(Min) = Mass flow rate per minute
H= Head in ft (I think)
G= Acceleration of gravity or 32ft per sec squared.

This seems to me like a falling water equation of some type which I want to get data from.

The question, in basic terms, that we would like to know is: How much potential or stored energy (in watts/hp/) would a 55gal barrel full of air have if it was tethered to the sea floor at a depth of 500ft? It seems like a non liner question. As the displacement of water column pushed the barrel upward the water column pressure would be reduced as the column got shorter on it assent, correct?


Thanks for helping us have fun with physics,
SQ

 

[russ_watters]

Via archemedes principle, displacement is not about pressure, it is about volume/mass displaced. So the only reason this problem becomes nonlinear is the compressibility of water - which is so low that you can safely ignore it. From there on out, you have a force and a distance...

 

[SimpleQuery]

Thank you so much for your feedback.

I certainly agree that the compressibility of water is a non issue for this discussion. So you're suggesting using force and distance to represent work?

Just so we're on the same page please permit the following example: the 55 gallon drum full of air sits in a tube with approximately the same inside diameter as the outside diameter of the barrel. The tube has been evacuated of water in the barrel is sealed in the tube similar in some regards to a piston with in a cylinder wall. The tube is just a theoretical guide. So in basic terms there would be approximately 86K PSI pushing up on the drum. Please take the example from the point and help us figure out how much energy would be involved when the barrel tether was released from the drum and it started its ascent to the surface as the surrounding water filled the column by rushing in behind the barrel and pushing it upward.

Thanks,
SQ