# Why does the pressure of a fluid in motion change?

1. Nov 10, 2014

Hi everyone,

I'm new here and I have a question to all the physicists out here in the forum.

I'm an aerospace engineering student and there is something that has been bothering me for
quite a while.

That is: Why does the static pressure of a fluid in motion change?

Don't get me wrong, I'm not a newbie in the area of fluid mechanics, aerodynamics and CFD.
I would say that I understand the principles of fluid flow and the laws governing fluid
motion pretty well. But what is really happening with the fluid when it accelerates and why
does the pressure, density and temperature change as a result?

So I need a microscopic view of the physics that's going on in a moving fluid parcel. I
attached a sketch of two fluid parcels. One standing still and the other accelerating. By
applying the equation of motion to the moving parcel I was able to derive the Bernoulli
equation and well, of course the pressure changes when the fluid is accelerating. The
pressure is the engine of fluid flow.

But how exactly do the single molecules in this parcel behave during the acceleration and
how does their motion contribute to changes of the flow properties?
Is the parcel streched by different speeds on its boundaries?

If you already know the answer then go for it and make me life easier :)
Thanks!

Here are my theories about what's going on in the fluid:

First of all of course the static pressure is the pressure that can be measured at a wall
normal to the stream or if the fluid is enclosed in a container the static pressure can be
felt on every wall. The pressure is induced by the single molecules that hit the wall.

So now I thought, that when a fluid starts to move the random motion of the molecules is
straightened and the velocity component of the molecules normal to the wall is decreased,
which results in a weaker impulse and hence a decreased static pressure at the wall. But
still this model is not really satisfying ...

Maybe at the same time the observed fluid parcel streches and simultaniously its height
decreases, just as a strip of metal would do under tension. So in total the volume would
increase which contributes to less pressure and density. However in an incompressible fluid
the height would just decrease so much so that the volume stays constant and so does the
density. But what's happening with the pressure?

Well, my thoughts are pretty incomplete...

I think if you have read this post till the end you can understand how desperatly I'm
searching for a solution.

I would really appreciate your help!

Cheers!

2. Nov 10, 2014

### Doug Huffman

Pressure is the conserved momentum force on the vessel wall. As the mass flux increases, the resultant perpendicular to the vessel wall diminishes.

3. Nov 11, 2014

Hi Doug,

Ok, so my initial thoughts were not too far off of whats happening.

So the velocity v of a fluid parcel would then be the average velocity of all the molecules together, right? Which means that if my fluid parcel is moving parallel to a wall less molecules will hit the wall, hence a lower pressure will be felt at the wall. Unfourtunately this is not fully satisfying me.

Let's say I am in the middle of a fluid parcel that stands still. Since molecules will hit me I will feel the static pressure. But what pressure will I feel if the parcel and I start to move with a velocity v?
I'm thinking about the resultant velocity of these molecules as the sum of an average velocity component and a fluctuating part, just as the Reynolds decomposition suggests it for turbulent flow. Is the fluctuating velocity component, which is the random motion of the molecules, still the same as before when the parcel was not moving? Or is this part reduced which would correspond to less molecules that hit me and hence a lower static pressure in the middle of the parcel?

I hope you can somehow understand what I mean...

Thanks!

4. Nov 11, 2014

### cjl

The static pressure of a moving parcel of fluid is not necessarily lower than the pressure of a stationary one. Bernoulli's relation is often misunderstood - it says that for an incompressible, inviscid flow, the total pressure 1/2ρV2+P is constant along a streamline as long as there is no energy addition or loss. If you accelerate a parcel of fluid, there could be energy addition, which means that this may not be valid.