Explain Bernoulli at the molecular level?

  • Context: Undergrad 
  • Thread starter Thread starter user079622
  • Start date Start date
Join the discussion
Registration is free. Ask a follow-up in this thread, or start your own.
Sign up Log in
252 replies · 13K views
user079622 said:
.... Bernoulli tell nothing about how pressure is exerted on walls, at molecular level(real physics behind pressure).
True. That's not what it is for.
user079622 said:
Yes I understand that total pressure = dynamic p. + static p. , Do I know how and when to use Bernoulli correctly? No
What exactly is it that you don't understand about how to apply Bernouuli's principle/equation to the situation described in the link in Post #4?
 
Physics news on Phys.org
russ_watters said:
True. That's not what it is for.

What exactly is it that you don't understand about how to apply Bernouuli's principle/equation to the situation described in the link in Post #4?
Bernoulli said......Total p.=static p. +dynamic p.

So if dynamic(speed) goes up, then static must go down to keep total p. constant. So people automatically remember if speed goes up, static goes down, and vice versa.
And than people wonder why static port in pitot tube, dont show drop in pressure as plane increase speed!! :)
 
user079622 said:
Bernoulli said......Total p.=static p. +dynamic p.

So if dynamic(speed) goes up, then static must go down to keep total p. constant. So people automatically remember if speed goes up, static goes down, and vice versa.
And than people wonder why static port in pitot tube, dont show drop in pressure as plane increase speed!! :)
Bernoulli's principle states: "The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant."
[insert standard assumptions here]

https://byjus.com/physics/bernoullis-principle/

That's for one packet of fluid traveling from one place to another (aka, along a streamline). That's what the principle/equation are about. When you're trying to use it to describe two separate situations (a car at rest vs a car in motion), that's not what it's about/for.

And that should be fairly obvious from looking at the equation: there's one term of static pressure and one term for velocity/velocity pressure, unless you are comparing two points along the same flow in which case there's up to two of each.
 
Reply
  • Like
Likes   Reactions: dextercioby and user079622
russ_watters said:
That's for one packet of fluid traveling from one place to another (aka, along a streamline).
If I choose two arbitrary points above the wing, how will I know if they lie on the same streamline?
 
@jbriggs444

If I somehow "capture" in theoretical box flow over the wing, inside the box I will have same number of molecules compare to box that I capture a freestream air? Of course density and temperature is constant.
 
user079622 said:
If I somehow "capture" in theoretical box flow over the wing, inside the box I will have same number of molecules compare to box that I capture a freestream air? Of course density and temperature is constant.
If you are holding density constant then of course a box of a fixed volume will always capture the same number of molecules.

What are you really trying to ask?
 
Reply
  • Like
Likes   Reactions: russ_watters
jbriggs444 said:
If you are holding density constant then of course a box of a fixed volume will always capture the same number of molecules.

What are you really trying to ask?
If there is same numbers of molecules that hitting the wall, how then explain why pressure is reduced?
I just want to tell that something with this pressure= "molecules bouncing the wall" is not logical.
 
russ_watters said:
When velocity rises.
Stretched in flow direction and contracted perpendicular to flow in the way, that volume of "control volume" keep the same?
 
user079622 said:
If there is same numbers of molecules that hitting the wall, how then explain why pressure is reduced?
I just want to tell that something with this pressure= "molecules bouncing the wall" is not logical.
You're mixing and matching from different scenarios now. A gas in a closed, rigid box is not moving relative to the box. Bernoulli's equation/principle does not apply inside the closed box.

The derivation of Bernoulli's equation is in the link I gave you in Post #33.

Note also: incompressible flow is a simplifying assumption used in the derivation that works in low speed (low compressibility) flow.
 
Reply
  • Like
Likes   Reactions: jbriggs444
russ_watters said:
That's for one packet of fluid traveling from one place to another (aka, along a streamline). That's what the principle/equation are about. When you're trying to use it to describe two separate situations (a car at rest vs a car in motion), that's not what it's about/for.

And that should be fairly obvious from looking at the equation: there's one term of static pressure and one term for velocity/velocity pressure, unless you are comparing two points along the same flow in which case there's up to two of each.
in 10:05h car drive 10km/h in 10:07h car drive 300km/h, at front is probe with static port in clean air.
Why are these two separate situations, why this case is not same as particle flow in pipe from big diameter to small diameter? (except this is atmosphere, not constrain by pipe walls)


Unted.webp
 
@user079622

I think it would be helpful if we tried to work off of this problem type I cooked up that attempt to examine the things you ask about in the OP.

Imagine you have a cart like this in still air. It is moving with a constant velocity to the right being propelled by a force ##F##. The control volume is the dashed boundary encasing the cart and the induced flow in the "vicinity" of the cart, where things are obviously changing. The frame labeled ##cv## is inertial. What questions can we help to answer on a model like this (please excuse the drawing)?

1746735037415.webp



P.S. at Mods. What is going on with the spell checking here. Its doesn't even try to make suggestions lately? It is killing me trying to remember how to spell things!
 
user079622 said:
in 10:05h car drive 10km/h in 10:07h car drive 300km/h, at front is probe with static port in clean air.
Why are these two separate situations, why this case is not same as particle flow in pipe from big diameter to small diameter? (except this is atmosphere, not constrain by pipe walls)


View attachment 360813
It is "like" pipe flow in the sense that the molecules bouncing off the cart are constrained by other molecules, which are constrained by more molecules etc... This is what I think anyhow. I don't know how a physicist reconciles this...as I think the pressure is independent of particle collision in an ideal gas. However, in a fluid model it makes perfect sense. So I am also intrigued to explore/discuss there as well.
 
user079622 said:
in 10:05h car drive 10km/h in 10:07h car drive 300km/h, at front is probe with static port in clean air.
Why are these two separate situations, why this case is not same as particle flow in pipe from big diameter to small diameter? (except this is atmosphere, not constrain by pipe walls)
?? The particles are kilometers apart.

But another answer is that this example is unsteady flow, and Bernoulli's Priinciple assumes steady flow. It's like if you have a fan powered Venturi tube and you are turning up the fan speed while reading different points in the tube. The readings will not satisfy Bernoulli's Principle/ conservation of energy because the mass flow rate at the first point will be higher. than at the second point.
 
erobz said:
It is "like" pipe flow in the sense that the molecules bouncing off the cart are constrained by other molecules, which are constrained by more molecules etc... This is what I think anyhow. I don't know how a physicist reconciles this...as I think the pressure is independent of particle collision in an ideal gas. However, in a fluid model it makes perfect sense. So I am also intrigued to explore/discuss there as well.
I'm pretty sure the detail here is that air is a gas and the devil is that the basic form of Bernoulli's Principle/equation assumes incompressible flow*. So you can't use a particle based gas model to explore the basic form of Bernoulli's. The basic form is technically wrong to apply to a gas, it's just not wrong enough to matter at low speed.

OP may prefer to jump straight to the compressible flow version to reconcile how a pressure can change without a change in volume, density or temperature, but then they haven't actually learned Bernoulli's Principle itself. That's not what it's about. As said in Post #6, it's just getting in the way of learning Bernoulli's Principle.

*Indeed, it was discovered through experiments with flowing water.
 
russ_watters said:
I'm pretty sure the detail here is that air is a gas and the devil is that the basic form of Bernoulli's Principle/equation assumes incompressible flow*. So you can't use a particle based gas model to explore the basic form of Bernoulli's. The basic form is technically wrong to apply to a gas, it's just not wrong enough to matter at low speed.

OP may prefer to jump straight to the compressible flow version to reconcile how a pressure can change without a change in volume, density or temperature, but then they haven't actually learned Bernoulli's Principle itself. That's not what it's about. As said in Post #6, it's just getting in the way of learning Bernoulli's Principle.

*Indeed, it was discovered through experiments with flowing water.
Well, I feel for the OP (and myself). Problems that show (relatively) simple relationships as examples inspire confidence that isn't really grounded in reality. They make you feel like you should be able to say something, but then you find so many blind spots the problem becomes intractable in just a shallow dig.

So the problem I contrived in post 45 seems to be "steady flow" to me. How do you feel about that?
 
Last edited:
Reply
  • Like
Likes   Reactions: russ_watters
russ_watters said:
?? The particles are kilometers apart.
If they are on same streamline, why does is matter?
russ_watters said:
But another answer is that this example is unsteady flow, and Bernoulli's Priinciple assumes steady flow. It's like if you have a fan powered Venturi tube and you are turning up the fan speed while reading different points in the tube.
Yes that is correct, I never think about it.
Frabjous said:
Maybe this discussion will help
https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/bernoullis-equation/#:~:text=The equation appears in many,a constant throughout the flow.
Quote from your source:
"If a gas is at rest, all of the motion of the molecules is random and the pressure that we detect is the total pressure of the gas. If the gas is set in motion or flows, some of the random components of velocity are changed in favor of the directed motion. The directed motion is called “ordered,” as opposed to the disordered random motion.

We can associate a “pressure” with the momentum of the ordered motion of the gas. We call this pressure the dynamic pressure. The remaining random motion of the molecules still produces a pressure called the static pressure."

I don't agree with this view, because it suggest if airflow travel at higher speed, random components of velocity is reduced so static pressure is reduced. We know that is not case, for reduction in static pressure we must have acceleration of flow, not constant velocity. Otherwise aircraft static port will show increase in altitude as he fly at higher speeds.
 
user079622 said:
Quote from your source:
"If a gas is at rest, all of the motion of the molecules is random and the pressure that we detect is the total pressure of the gas. If the gas is set in motion or flows, some of the random components of velocity are changed in favor of the directed motion. The directed motion is called “ordered,” as opposed to the disordered random motion.

We can associate a “pressure” with the momentum of the ordered motion of the gas. We call this pressure the dynamic pressure. The remaining random motion of the molecules still produces a pressure called the static pressure."

I don't agree with this view, because it suggest if airflow travel at higher speed, random components of velocity is reduced so static pressure is reduced. We know that is not case, for reduction in static pressure we must have acceleration of flow, not constant velocity. Otherwise aircraft static port will show increase in altitude as he fly at higher speeds.
It would be clearer, if they stated the condition as:... if the gas accelerates relative to an inertial frame of reference.

Then you need a real non-zero net force on the air packets, and thus a pressure gradient.
 
Reply
  • Like
Likes   Reactions: user079622
A.T. said:
It would be clearer, if they stated the condition as:... if the gas accelerates relative to an inertial frame of reference.

Then you need a real non-zero net force on the air packets, and thus a pressure gradient.

If we have case where air blower blow air in atmosphere. If I increase power of blower in time interval A to B, from 10% to 100%, airflow is accelerated in this time interval, so there is positive pressure gradient in flow direction.
(Here we can't use Bernoulli, because it is unsteady flow.)
If I put pitot-static tube in front of air nozzle, what will static port show in this time interval?

250px-Pitot_tube_types.svg.webp
 
user079622 said:
I don't agree with this view, because it suggest if airflow travel at higher speed, random components of velocity is reduced so static pressure is reduced. We know that is not case, for reduction in static pressure we must have acceleration of flow, not constant velocity. Otherwise aircraft static port will show increase in altitude as he fly at higher speeds.
For an ideal gas, P is proportional to density and temperature. If P drops, T must also drop for low speed (negligible density change, <.3 sound speed) flows.
 
Last edited:
user079622 said:
If I put pitot-static tube in front of air nozzle, what will static port show in this time interval?
View attachment 360838
I don’t understand your scenario and what interval you mean. You need a steady flow in an inertial reference frame.
 
A.T. said:
I don’t understand your scenario and what interval you mean. You need a steady flow in an inertial reference frame.
Yes I know, but I do unsteady flow deliberately , here airflow speed increase during measurement. Will static port read lower pressure that atmospheric pressure?
 
user079622 said:
Yes I know, but I do unsteady flow deliberately , here airflow speed increase during measurement. Will static port read lower pressure that atmospheric pressure?
My intuition is that the static pressure would be higher than atmospheric in the impact zone(front of the vehicle). What is your opinion, or anyone?

If the car is sitting still in still air, atmospheric pressure registers on the gauge. If it starts forward motion a normal force develops on the car, that normal force is also acting on the flow via Newtons Third Law. I expect that normal force distributes over the front to the wedge in addition to atmospheric pressure.

1746791219230.webp



$$ P_{gauge} \approx P_{atm} + \frac{N \sin \theta }{A_1} $$
 
Last edited:
user079622 said:
Yes I know, but I do unsteady flow deliberately
Why? It's more complicated to solve and requires more specifications.
 
Reply
  • Like
Likes   Reactions: russ_watters
A.T. said:
Why? It's more complicated to solve and requires more specifications.
To see how probe react to accelerated flow.

erobz said:
My intuition is that the static pressure would be higher than atmospheric in the impact zone(front of the vehicle). What is your opinion, or anyone?
In my test there is no impact zone.

In your test from post #45, yes some distance in front of car is higher pressure than atmospheric. The highest pressure is at stagnation point.
 

Similar threads

Can you please explain Bernoulli's equation?
  • Callmelucky
  • · Replies 61 ·
  • Introductory Physics Homework Help
3
Replies
61
Graduate Exactly how do pressure waves work at the molecular level?
  • Freixas
  • · Replies 49 ·
  • Mechanics
2
Replies
49
Nozzle/Turbine at the Molecular Level
  • HungryX2Hippo
  • · Replies 2 ·
  • Aerospace Engineering
Replies
2
Undergrad Tension force at molecular level
  • attentater
  • · Replies 1 ·
  • Mechanics
Replies
1