What causes pressure and is it isotropic in a moving fluid?

[Fountains]

I'm studying fluid dynamics and we just had a lecture about the momentum equation. We started the lecture by talking about pressure in terms of molecules moving across a hypothetical surface element and carrying their momentum with them (in both directions). There are 2 things confusing me about this:

1) we said the pressure is isotropic, but given I'm studying fluid dynamics, with this description it seems pretty clear that the pressure will point in the direction of the fluid velocity, and in a direction normal to that there will be (on average) no molecules moving in that direction so what would cause the pressure?

2) When deriving the momentum equation, we then also included the effect of momentum entering and leaving our arbitrary volume, but this seems to be exactly what we described pressure to be at the start of the lecture. So I think I have misunderstood the root cause of pressure: eg. is it particles colliding or just moving between regions and transferring momentum?

I have been thinking about this in frustration for hours now so any help would be appreciated!

 

[Chestermiller]

There are two parts to the motion of the molecules in the fluid. For the most part, the different molecules are moving randomly in all different directions, and this gives rise to the isotropic feature. But, in addition to this, there is organized motion of the molecules that averages out to what we observe macroscopically as the "velocity of the fluid." This motion is not isotropic, and gives rise to the additional momentum flux in the differential momentum balances that is not isotropic.

 

[SirCurmudgeon]

Hi,

About pressure in a fluid. Pressure is a property at a point in a fluid. Some define pressure using a fluid/solid boundary or interface.
Suppose you have water in a cubical container on a table. On one side (say the right side) fluid water molecules impact the boundary
and rebound. Momentum exchange happens. That exchange per unit of area (force per area) is pressure. Defined at a fliud/solid interface.

Now, consider the horizontally left side of the water/container. This is a boundary also. Water momentum and area are pressure again.
So we have pressure defined at the left interface and right interface. Next we conclude pressures exists as a property of the fluid for
all points between the walls and at all points in fluids.

Also be careful about the word "static." Static can mean "not moving." It is better to think os static as "undisturbed."
Hence motion at constant velocity is "static."

http://www.thermospokenhere.com/wp/02_tsh/B0600___wilma_static/wilma_static.html

JP

 

[Chestermiller]

Hi,

About pressure in a fluid. Pressure is a property at a point in a fluid. Some define pressure using a fluid/solid boundary or interface.
Suppose you have water in a cubical container on a table. On one side (say the right side) fluid water molecules impact the boundary
and rebound. Momentum exchange happens. That exchange per unit of area (force per area) is pressure. Defined at a fliud/solid interface.

Now, consider the horizontally left side of the water/container. This is a boundary also. Water momentum and area are pressure again.
So we have pressure defined at the left interface and right interface. Next we conclude pressures exists as a property of the fluid for
all points between the walls and at all points in fluids.

Also be careful about the word "static." Static can mean "not moving." It is better to think os static as "undisturbed."
Hence motion at constant velocity is "static."

http://www.thermospokenhere.com/wp/02_tsh/B0600___wilma_static/wilma_static.html

JP

Even if the fluid is not moving at constant velocity, the term “static pressure” is often used in place of of the word pressure. Both terms are used interchangeably, and describe the isotopic part of the stress tensor.

 

[Fountains]

Thanks! I think I understand the concept now in terms of kinetic theory, like this https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Pressure_and_kinetic_energy , but I'm having trouble squaring this with the equation rho*g*h often given for the pressure in a liquid at depth h: the second equation implies that the pressure at the surface would be zero, but for a non-viscous fluid their may still be tangential velocity at the surface causing pressure right (by kinetic theory) so there should still be pressure just due to the molecules having energy? Is the issue just that this acts like a constant which is added everywhere so can be ignored given we often talk only about pressure gradients?

 

[Chestermiller]

Thanks! I think I understand the concept now in terms of kinetic theory, like this https://en.wikipedia.org/wiki/Kinetic_theory_of_gases#Pressure_and_kinetic_energy , but I'm having trouble squaring this with the equation rho*g*h often given for the pressure in a liquid at depth h: the second equation implies that the pressure at the surface would be zero, but for a non-viscous fluid their may still be tangential velocity at the surface causing pressure right (by kinetic theory) so there should still be pressure just due to the molecules having energy? Is the issue just that this acts like a constant which is added everywhere so can be ignored given we often talk only about pressure gradients?

Sorry. I don't get the gist of this question. Are you talking about a free surface where the liquid is in contact with the air?

 

[Fountains]

Sorry. I don't get the gist of this question. Are you talking about a free surface where the liquid is in contact with the air?

Yes sorry-perhaps this is not so related to fluid dynamics-it isn't in my lecture notes but it just seemed to keep coming up whenever I looked up pressure!

 

[Chestermiller]

Yes sorry-perhaps this is not so related to fluid dynamics-it isn't in my lecture notes but it just seemed to keep coming up whenever I looked up pressure!

At a free surface with air, the pressure at the boundary is equal to the atmospheric pressure $p_a$. So the equation should really be $p=p_a+\rho gh$ rather than $p=\rho gh$. When we write the equation the latter way, what we are referring to is the so-called "gauge" pressure, which is the absolute pressure minus the atmospheric pressure.

 

[PeroK]

I'm studying fluid dynamics and we just had a lecture about the momentum equation. We started the lecture by talking about pressure in terms of molecules moving across a hypothetical surface element and carrying their momentum with them (in both directions). There are 2 things confusing me about this:

1) we said the pressure is isotropic, but given I'm studying fluid dynamics, with this description it seems pretty clear that the pressure will point in the direction of the fluid velocity, and in a direction normal to that there will be (on average) no molecules moving in that direction so what would cause the pressure?

2) When deriving the momentum equation, we then also included the effect of momentum entering and leaving our arbitrary volume, but this seems to be exactly what we described pressure to be at the start of the lecture. So I think I have misunderstood the root cause of pressure: eg. is it particles colliding or just moving between regions and transferring momentum?

I have been thinking about this in frustration for hours now so any help would be appreciated!

Velocity is frame dependent. The same fluid could be seen as moving at any speed, depending on your frame of reference. If you force a surface though a fluid, then you feel a resisting force that is more than the static fluid pressure at each point.

The pressure of a fluid should be defined in the rest frame of the fluid.

 

[Chestermiller]

Velocity is frame dependent. The same fluid could be seen as moving at any speed, depending on your frame of reference. If you force a surface though a fluid, then you feel a resisting force that is more than the static fluid pressure at each point.

The pressure of a fluid should be defined in the rest frame of the fluid.

As a guy with lots of fluid mechanics experience, I don't follow this. Are you saying that fluid pressure exists only at a solid surface?

 

[PeroK]

As a guy with lots of fluid mechanics experience, I don't follow this. Are you saying that fluid pressure exists only at a solid surface?

No, just that in the OP's view of the pressure increasing with velocity, you could increase the fluid pressure simply by looking at the fluid in a different reference frame - one where it is moving very fast, for example.

Or, alternatively, by forcing something through the fluid and calling the resisting force "pressure", which I think is what the OP is thinking.

 

[Chestermiller]

No, just that in the OP's view of the pressure increasing with velocity, you could increase the fluid pressure simply by looking at the fluid in a different reference frame where it is moving.

Or, by forcing something through the fluid and calling the resisting force "pressure", which I think is what the OP is thinking.

Oh. That wasn't my interpretation.

 

[PeroK]

Oh. That wasn't my interpretation.

It was this bit here:

1) we said the pressure is isotropic, but given I'm studying fluid dynamics, with this description it seems pretty clear that the pressure will point in the direction of the fluid velocity,

But, fluid velocity is frame dependent, was really my only point.

 

[Chestermiller]

It was this bit here:
But, fluid velocity is frame dependent, was really my only point.

I think he was referring to differences in momentum between fluid entering a control volume through one surface and fluid leaving the control volume through another surface.

 

[Fountains]

I think he was referring to differences in momentum between fluid entering a control volume through one surface and fluid leaving the control volume through another surface.

I was just unsure as to whether the velocities were being measured in the frame of the fluid velocity or a rest flame, since it was not stated in my notes, but your first comment made me realize that it was as measured traveling with the fluid, so I think I get that now thanks.
But for future reference, it's "she"!