# Pressure change when volume changes for incompressible fluid

• Chris F
In summary, a user is seeking help with a fluid mechanics problem involving calculating the pressure increase in a closed tube filled with water when it is crushed. They mention the relevant equations and their understanding that the fluid can be considered static and incompressible. Another user suggests looking up the bulk compressibility of water, but notes that a 10% decrease in volume is unlikely. The original user explains that they are using a press and a die for a hydroforming operation and the 10% decrease is a rough approximation. They confirm that they can rearrange the equation to solve for dP using the given values.

## Homework Statement

Hi guys,

My first post here, I hope someone can help me out with a quick fluid mechanics problem.

I'm looking to calculate the pressure increase inside a closed tube full of water when the tube is crushed and therefore its volume reduced.

The tube is filled completely with water and pressurised to a nominal pressure of 10 bar. The starting volume is 2.1l and the volume after crushing is 90% of the initial volume.

2. The relevant equations

The tube remains sealed at all times so I think I can consider the fluid to be static and as its water, incompressible. However I am struggling to find the relevant equation to allow me to calculate the new pressure. All the static problems i have seen are concerned with open containers.

Can anyone help?

Thanks,

Chris

Look up the BULK COMPRESSIBILITY of water. But a 10% decrease in volume seems very unlikely.

Chet

Chestermiller said:
Look up the BULK COMPRESSIBILITY of water. But a 10% decrease in volume seems very unlikely.

Chet

Ok thanks, so i can rearrange to solve for dP using the values i quoted above?

Sorry i should probably explained more thoroughly, I am crushing the tube with a press into a machined die as part of a hydroforming operation, the 10% is a rough approximation using the shape of the die as an indication of the form the tube will take.

Thanks,

Chris

Chris F said:
Ok thanks, so i can rearrange to solve for dP using the values i quoted above?Chris
yes.

Hi Chris,

It sounds like you are dealing with a situation where the volume of an incompressible fluid, in this case water, is changing due to external pressure. In this scenario, the pressure inside the closed tube will indeed increase as the volume decreases. This can be explained by the relationship between pressure and volume for incompressible fluids, known as Boyle's Law.

Boyle's Law states that for an incompressible fluid, the pressure and volume are inversely proportional, meaning that as one increases, the other decreases and vice versa. In your case, as the volume is reduced to 90% of its initial value, the pressure inside the tube will increase by a factor of 10/9, or approximately 1.11 times the initial pressure.

To calculate the new pressure, you can use the equation P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume. Plugging in the values given in your problem, we get:

10 bar * 2.1 L = P2 * 0.9 * 2.1 L

Solving for P2, we get a final pressure of approximately 11.1 bar.

I hope this helps with your problem. Let me know if you have any further questions.

Best,

## 1. What is an incompressible fluid?

An incompressible fluid is a fluid that does not change in volume when subjected to changes in pressure. This means that the density of the fluid remains constant regardless of the applied pressure.

## 2. How does pressure change affect the volume of an incompressible fluid?

In an incompressible fluid, pressure changes do not affect the volume of the fluid. This is because the fluid is unable to be compressed, so it maintains its original volume regardless of the applied pressure.

## 3. What happens to the pressure of an incompressible fluid when its volume changes?

In an incompressible fluid, the pressure remains constant when the volume changes. This is because the fluid cannot be compressed, so the pressure is evenly distributed throughout the fluid at all times.

## 4. What is the relationship between pressure and volume in an incompressible fluid?

In an incompressible fluid, the pressure and volume have an inverse relationship. This means that as the volume of the fluid increases, the pressure decreases, and vice versa. However, this relationship only holds true for changes in volume, as the pressure remains constant in an incompressible fluid.

## 5. Are there any real-life examples of incompressible fluids?

Yes, there are many real-life examples of incompressible fluids. Some common examples include water, oil, and blood. These fluids are often used in hydraulic systems where pressure changes are used to control movement or perform work without changing the volume of the fluid.