# How much energy can be extracte from compressed water?

• antonima
In summary, the conversation discusses the possibility of using compressed water at high pressure to extract energy from the ocean. It is determined that at a depth of 4 km, the water would be compressed by 1.8%, releasing 0.36 MJ of energy if a valve is opened. However, it is also concluded that the energy required to raise the container holding the water would cancel out the energy extracted, making it an inefficient method for energy production.

#### 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?

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

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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

Nice that it fits! :)

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

The amount of energy that can be extracted from compressed water depends on various factors such as the initial pressure, volume, and temperature of the water. In this scenario, we have 1 ton of compressed water at 40 mega pascals and a volume of 982 liters. Assuming that the water is at standard temperature and pressure, the amount of kinetic energy that will flow out of the system when a valve is opened can be calculated using the Bernoulli's equation.

According to the Bernoulli's equation, the kinetic energy (KE) of a fluid is equal to half of its density (ρ) multiplied by the square of its velocity (v). Therefore, the amount of kinetic energy that will flow out of the system can be calculated as:

KE = 1/2 * ρ * v^2

To determine the density of the compressed water, we can use the ideal gas law, which states that the pressure (P), volume (V), and temperature (T) of a gas are related by the equation PV = nRT, where n is the number of moles and R is the gas constant. Since we know the volume and pressure of the compressed water, we can determine its density using this equation.

Assuming that the temperature is 25°C (298 K) and the gas constant is 0.0821 L*atm/mol*K, the number of moles of water can be calculated as:

n = PV/RT = (40 MPa * 982 L) / (0.0821 L*atm/mol*K * 298 K) = 1.6 moles

Now, we can determine the density of the compressed water as:

ρ = n/m = 1.6 moles / 0.982 L = 1.63 moles/L

Substituting this value into the equation for kinetic energy, we get:

KE = 1/2 * 1.63 moles/L * v^2

To determine the velocity of the water, we can use the continuity equation, which states that the product of the cross-sectional area (A) and the velocity (v) of a fluid is constant. Since we know the initial volume and the final volume (when the valve is opened), we can calculate the velocity of the water as:

v = (initial volume / final volume) * v = (982 L / 0.982 L) * v = 1000

## 1. How is energy extracted from compressed water?

The energy from compressed water can be extracted through a process known as hydraulic fracturing or "fracking." This involves injecting high-pressure water into underground rock formations to create fractures and release the natural gas or oil trapped within.

## 2. What is the potential amount of energy that can be extracted from compressed water?

The potential amount of energy that can be extracted from compressed water varies greatly and depends on various factors such as the location, depth, and quality of the rock formations. However, it is estimated that a single well can produce enough energy to power an average household for 25 years.

## 3. Are there any environmental concerns with extracting energy from compressed water?

Yes, there are several environmental concerns associated with extracting energy from compressed water. The process of hydraulic fracturing can contaminate groundwater and release methane gas, a potent greenhouse gas, into the atmosphere. There are also concerns about the disposal of wastewater and the potential for earthquakes caused by the injection of water into the ground.

## 4. Is compressed water a renewable source of energy?

No, compressed water is not considered a renewable source of energy. While the water itself is renewable, the process of extracting energy from it through hydraulic fracturing is not sustainable and can have negative impacts on the environment.

## 5. How does the energy extracted from compressed water compare to other energy sources?

The energy extracted from compressed water is comparable to other fossil fuels such as oil and natural gas. However, it is not as efficient or cost-effective as renewable energy sources like solar or wind power. Additionally, the environmental impacts of extracting and using compressed water for energy must also be taken into consideration.