# Static pressure

1. Apr 12, 2004

### leonpalios

When air flows through a variable cross - section tube, as the cross - section area increases, the average flow speed of air decreases (due to continuity equation) and according to Bernoulli’s theorem the static pressure increases. Regardless of the mathematical proof of Bernoulli’s theorem, what physical process causes the static pressure increase?
What physical process causes the static presssure decrease when the air speeds up passing through a narrow part of the tube?

2. Apr 12, 2004

### enigma

Staff Emeritus
Static pressure is caused by random motion of the particles in all direction.

Static pressure drops when you take away some of the random motion by 'converting' it into a directed motion.

3. Apr 14, 2004

### leonpalios

Explanation with more details (by me):

As the air speeds up passing through a narrow part of a tube, a portion of internal energy due to thermal motion of molecules converted in ordered kinetic energy (and thus the dynamic pressure increase).

The result of this is the decrease of radom kinetic energy of molecules in all directions other than the direction of flow. So the components of velocities in these directions is reduced too, and therefore the static pressure drops.

Is it a correct explanation?

4. Apr 14, 2004

### enigma

Staff Emeritus
Yep. AFAIK, that's it.

5. Apr 21, 2004

### leonpalios

To sum up:
As the air reaches at a region of the tube with a smaller cross-section area, the collisions among the molecules organize the velocities of the molecules in order for them to pass through the narrower part. This fact has the results below:
i) First of all the air is accelerated.
ii) Because the internal energy of the air due the thermal motion remains constant, the dynamic pressure increace and the static pressure drops.

A. If all the above are correct, does anybody know any reliable textbooks (graduate level) or articles that deal with them analytically and with accuracy, so to be sure that all of them are really correct?
B. Do the same things exists in the case that inside the tube liquid flows instead of air, when the thermal motion is decreased more?
C. As we say the accelaration of an amount of air causes static pressure drop. Contrarily, many textbooks/articles it is refered that the pressure gradients generates acceleration. But which pressure, static, dynamic or total?
What is finally correct? Pressure gradients generates acceleration or accelaration generates pressure gradients?
D. In which textbooks may I find the formula that associates the static pressure at a point and the flow speed in the same point? (I’m not refering to Bernoulli’s equation that associates the static pressure and the air speed at a point with the static pressure and the air speed at another point). I suppose that this formula arises by applying the laws of kinetic theory or statistical mechanics or thermodynamics.

6. Apr 21, 2004

### kurious

The pressure drops because the average angle at which air molecules strike the side of the tube gets less with increasing flow rate.

7. Apr 26, 2004

### Goethe3

And also if the molecular random kinetic energy decreases, the temperature where the static presure is lowest must also decrease, by definition.