Delay of propagation of the pressure in a fluid

• Gh778
In summary, the conversation discusses the concept of torque generated by a sudden increase in pressure inside a rotating disk full of liquid. The participants discuss the possibility of a torque being produced due to the delay in propagation of pressure and try to find a connection between density and force. The question arises from an exercise in a book and there is a debate about whether the fluid in question is a liquid or a gas.
Gh778

Homework Statement

Does the delay of propagation of pressure gives a torque during a short time ?

A disk full of a liquid turns at a constant angular velocity w around the red axis. At a time, a valve move out, this will increase quickly the pressure inside the liquid.

1/ Draw the lines of equal pressure from the valve
2/ Draw the forces from this additionnal pressure
3/ Is there an additionnal torque ?

Homework Equations

Speed of sound in the fluid

The Attempt at a Solution

1/ & 2/

3/ Yes, the torque from F1 is greater than F2

Is it correct ?

It might help to think of a different model. Instead of a fluid and valve, suppose there is a strut angled across inside the disc, connecting the points on the periphery where you show F1 and F2. Under some influence, heat maybe, the strut attempts to expand, exerting pressure on the disc edges. Would there be a torque on the disc?

I'm not sure, but I can explain the torque like this :

Increase the pressure inside the disk is like launch small balls in all directions. The energy from the spring (or heating) goes to the kinetic energy when balls change their velocity and there is heating too because there are collisions on the wall. The wall of the disk will receive collisions on the curved line ##(a,w)## after the line ##(b,x)##, after ##(c,y)## and after ##(d,z)##. If I look at the line ##(d,z)##, the wall of the disk receive a force that I noted ##F##, the torque is ##+Fd_1-Fd_2##, it's not 0. and it's the same for the others lines. If I make the comparaison with a translation, "balls" that collide the wall at points ##d## and ##z## transform their energy in heating, and forces canceled themselves. Here, the forces give 2 different moments.

Gh778 said:
I'm not sure, but I can explain the torque like this :

Increase the pressure inside the disk is like launch small balls in all directions. The energy from the spring (or heating) goes to the kinetic energy when balls change their velocity and there is heating too because there are collisions on the wall. The wall of the disk will receive collisions on the curved line ##(a,w)## after the line ##(b,x)##, after ##(c,y)## and after ##(d,z)##. If I look at the line ##(d,z)##, the wall of the disk receive a force that I noted ##F##, the torque is ##+Fd_1-Fd_2##, it's not 0. and it's the same for the others lines. If I make the comparaison with a translation, "balls" that collide the wall at points ##d## and ##z## transform their energy in heating, and forces canceled themselves. Here, the forces give 2 different moments.
OK, but consider what is firing these balls. There will be a reaction on that. What will happen to it?

The "spring" for example or the valve is firing the balls.

Reaction from the device that launch the balls ? In the rotation, the valve receives the force ##F_v##, this force increases the torque too (counterclockwise rotation):

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If someone could say if there is or not a torque and explain ?

Maybe I don't explain my thoughts enough. When the valve is moving quickly, the sum of force is always at 0, so the sum of torque must be at 0. But the density is changing with the speed of sound and the density is not the same at start because there is centrifugal forces in the liquid, the wave of pressure don't change the force but change the density, does this density changes the force on one part more than another part ? The force of pressure depend of the force and the "surface" and with a lower density there is less surface so less pressure. With a gas, it's possible to imagine more molecule at outer radius and less molecules at inner radius. When the valve pushes molecules, there are more molecules push at outer than at inner. So why the pressure could be the same and so the force and the torque ? I don't find a link where the density is link to the force.

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This is a most unusual question. Where does it come from?

I saw this exercice in a book, why ?

Gh778 said:
I saw this exercice in a book, why ?
I feel one needs to know more about the subject matter of the book.
Usually liquids are considered incompressible, but in that theoretical view there can be no propagation delay. The problem title says fluid, but the text says liquid - which is it? Gases are fluids too.

1. What is meant by "delay of propagation of the pressure in a fluid"?

The delay of propagation of the pressure in a fluid refers to the time it takes for a change in pressure at one point in the fluid to be transmitted to other points in the fluid. This delay occurs due to the compressibility and viscosity of the fluid, which cause the pressure to propagate at a finite speed.

2. How does the delay of propagation of pressure affect fluid dynamics?

The delay of propagation of pressure can have a significant impact on fluid dynamics, as it can affect the behavior of the fluid in response to external forces. For example, in a closed system, a sudden change in pressure at one point can cause a delay in the response of the fluid, resulting in oscillations or changes in flow rate.

3. What factors can influence the delay of propagation of pressure in a fluid?

The delay of propagation of pressure is influenced by several factors, including the compressibility and viscosity of the fluid, the distance between the points of pressure change, and the geometry of the system. Additionally, the type of fluid and the presence of any obstacles or boundaries can also affect the delay.

4. Can the delay of propagation of pressure be reduced or eliminated?

While the delay of propagation of pressure cannot be completely eliminated, it can be reduced by using less compressible fluids or increasing the viscosity of the fluid. Additionally, optimizing the geometry of the system and minimizing the distance between points of pressure change can also help reduce the delay.

5. How is the delay of propagation of pressure measured or calculated?

The delay of propagation of pressure can be measured or calculated using various methods, such as pressure transducers, flowmeters, and mathematical models. These methods take into account the fluid properties, system geometry, and external forces to determine the delay in pressure propagation.

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