Isothermal Expansion of Water/Moving Boundary

In summary, the conversation discusses the behavior of water in a closed system with one moving boundary. The speaker is wondering about the effect on pressure when the boundary is moved, and whether this could be used to create a suction cup-like device. There is also a discussion about the possibility of cavitation and the feasibility of using a linear servo to create the desired pressure drop.
  • #1
WeirdWater
2
0
Hello all,

I've been wondering how water reacts in a closed, rigid system with one moving boundary. Assuming the system is perfectly filled with water, and one side of the boundary moves (increasing the volume), how does this affect the pressure in the system?

Since water is incompressible, I would think that moving one boundary would dramatically increase the pressure on the other boundaries within the container (since the water attempts to maintain its original volume). However, I don't get how to modify the formulas for Bulk Modulus to prove this is true.

I want to create a water-filled probe that rests on the skin and then move a boundary of that probe to raise the skin. In my mind, this should act much like a reverse hydraulic lift, forcing the skin to lift as the other boundary is drawn away. However, I don't know this with certainty and I don't get how to show this relation in exact, quantitative terms. I would appreciate any help that could be provided in modelling this system to be as realistic as possible.

Thanks for your help!
 
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  • #2
The system is subject to some external pressure, usually atmospheric. Initially, the internal pressure may be taken equal to the external. As the volume starts to expand,the internal pressure will start dropping off very rapidly, because water's volume does not change much under pressure, and at same stage a cavity will form there. The cavity will not be completely evacuated, it will contain water vapor. The pressure on all the boundaries will never exceed the external (atmospheric) pressure.

If I understand your description correctly, what you are thinking about is basically a suction cup. It could be somewhat more efficient than a typical suction cup, but not in a major way.
 
  • #3
So then I do need to worry about cavitation? The maximum force I was hoping to exert on the skin is about 7N, or an internal pressure about 50kPa below atmospheric, so I had hoped that moving the boundary could accomplish this. Is there a way I could do this effectively with a linear servo as the drive and then have the skin directly acted on by the water pressure while avoiding cavitation?

Since the cavitation pressure of water is lower than its equilibrium vapor pressure (~3kPa), I thought there wouldn't be cavitation unless the system featured significant cavitation nuclei?
 
  • #4
Water's bulk modulus is 2.2 GPa, which is quite high. That means you the pressure vessel must be quite large, so that even a low-precision servo could do it. Let's say the vessel contains one liter = 0.001 m^3 of water. Then the change in the volume is 2.3E-8 m^3. If your vessel has, say, a 10-mm long, 1-mm radius cylinder, then a piston would need to move 7.2 mm in that cylinder to create a 50 kPa pressure drop. I think this is quite achievable with modern servos.
 
  • #5


I find this topic interesting and would like to provide some insight into the isothermal expansion of water with a moving boundary. First, let's define isothermal expansion as a process where the temperature of a system remains constant while its volume increases. In this scenario, we are assuming that the water is in a closed, rigid system and only one boundary is moving to increase the volume of the water.

Based on the ideal gas law, we know that pressure and volume are inversely proportional at a constant temperature. However, this law does not apply to liquids such as water, which are incompressible. So, how does the pressure change in this scenario?

To answer this question, we need to consider the concept of bulk modulus. Bulk modulus is a measure of a material's resistance to compression under pressure. For liquids, it is defined as the ratio of pressure to the fractional decrease in volume. In other words, it is a measure of how much a liquid's volume changes under pressure.

In the case of water, its bulk modulus is very high, meaning that it is difficult to compress and its volume remains relatively constant even under high pressure. This is why we often consider water to be incompressible.

Now, let's apply this concept to our scenario of a moving boundary in a closed, rigid system filled with water. As the boundary moves and increases the volume of the water, the bulk modulus of water will resist this change in volume. This means that the pressure in the system will increase, as the water is unable to compress and maintain its original volume.

In terms of your proposed experiment with the water-filled probe and skin, it is possible that the reverse hydraulic lift effect could occur. However, it would depend on the specifics of the probe and the skin, as well as the amount and rate of pressure applied. It would be necessary to model and test this scenario to determine the exact quantitative relationship between the movement of the boundary and the resulting pressure and lift on the skin.

In summary, the isothermal expansion of water with a moving boundary would result in an increase in pressure within the closed, rigid system due to the high bulk modulus of water. More research and experimentation would be needed to fully understand the relationship between this process and its potential applications. I hope this helps provide some insight into this topic.
 

What is isothermal expansion of water/moving boundary?

Isothermal expansion of water/moving boundary is a thermodynamic process in which the volume of water increases while its temperature remains constant. This can occur when heat is added to the system and the water expands without changing its temperature.

What is the significance of isothermal expansion of water/moving boundary?

The significance of isothermal expansion of water/moving boundary lies in its application in various industrial processes, such as in refrigeration and air conditioning systems. It also helps in understanding the behavior of water under different conditions and in predicting the properties of water in these processes.

What factors affect the isothermal expansion of water/moving boundary?

The isothermal expansion of water/moving boundary is affected by several factors, including pressure, temperature, and the properties of the water itself. The presence of impurities or dissolved gases in water can also affect its expansion behavior.

What is the difference between isothermal expansion and adiabatic expansion of water/moving boundary?

The main difference between isothermal expansion and adiabatic expansion of water/moving boundary is the change in temperature. In isothermal expansion, the temperature remains constant, while in adiabatic expansion, the temperature changes due to the absence of heat transfer.

How is the isothermal expansion of water/moving boundary measured?

The isothermal expansion of water/moving boundary can be measured by using various methods, such as volume displacement, dilatometer, or by calculating the thermal expansion coefficient. These methods involve measuring the change in volume or temperature of the water as it undergoes expansion.

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