How much energy can be extracte from compressed water?

[antonima]

Say I have 1 ton of compressed water at 40 mega pascals, IE its volume is only 982 liters. At standard temperature and pressure, how much kinetic energy will flow out of this system if a valve is opened?

 

[I like Serena]

Welcome to PF, antonima!

Let's see.

I think we're talking about a release of 0.36 MJ in energy, of which part will be kinetic energy.
The volume that comes out is 18 L (assuming no change in temperature).We would need the compressibility of water for this:
$$\beta = -{1 \over V} {\partial V \over \partial P}$$

The change in volume (the water spewing out) is:
$$\Delta V = -\beta V \Delta P$$

The energy that is released by the expansion to standard pressure is:
$$W = \int PdV = \int P \cdot -\beta V dP = -{1 \over 2} \beta V P^2 |_{P_1}^{P_2}$$

At T=25 °C, we have:
β = 4.6 x 10^-10 m²/N
V = 0.982 m³
P1 = 40 MPa
P2 = 100 kPa

This means W=0.36 MJ and ΔV=0.018 m³

 

[antonima]

Hi ILS!

.36 MJ. I like that!
See, I have been learning about oceanography and how water compresses in the deeper parts of the ocean. At 4 km in depth, or 40 MPa water is compressed by 1.8%. I was thinking that maybe it could be sealed in a container which would keep it pressurized and raised to extract energy from the deep ocean.

Funny enough, to raise this water would at the very minimum require
(buoyancy at top - buoyancy at bottom * 1/2) * gravity * height
(basically using mass*gravity*height)
(18*1/2*4000*9.81) = .353 MJ !
This is not counting friction, drag, or the energy required to raise the container which carries the water. It seems that the thermodynamics of this all works out so no energy is created, and energy cannot be continuously extracted from the ocean.

Your equation also agrees with the the pressure analysis. Pressure is just Newtons/meter squared. If water were to be a cube just short of 1 meter squared, it would expand ~1.8 cm to one side.
40,000,000 pascals *.5*.018 m = .36 MJ !
using
Force*distance

 

[I like Serena]

Nice that it fits! :)

And pity that we can't extract energy this way. :(