# Bernoulli : temperature lower in a restriction?

## Main Question or Discussion Point

Hello
I’ d like to have your thoughts about any temperature variation when a fluid passes through a narrower part of a tube, a subject quite rarely discussed..

Can we start with « perfect Bernoulli conditions »and an incompressible fluid having only translational energy,. flowing theough a perfectly insulated tube. When the fluid passes through the restriction, we can assume I believe that an average molecule’s total energy is unchanged. Although the energy is more concentrated along the direction of the tube,can we assume that energy exchange with the walls of the narrower part of the tube will be unchanged ? And that there will be no temperature change ?

Now the fluid is hotter than the surrounding air and the tube is not insulated. When the fluid passes through the narrower part of the tube, can we assume that as collisions of molecules against the walls of the tube are less frequent, that energy transfer from the hot fluid to the colder wall will be reduced and that therfore the walls of the narrower part of the tube will be colder ?

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rcgldr
Homework Helper
In the idealized Bernoulli example, the assumption is that no work of any kind is done on the fluid, so the internal kinetic energy (including density component) doesn't change, so the temperature would be constant.

In the real world, when pressure is reduced, temperature normally drops, but in the real world you'd also have some amount of compression effects, viscous drag with the sides of the walls of a pipe, ... I'd be a bit curious about temperature effect on flow through a propeller or rotor, (low pressure fore of the prop, high pressure aft) but haven't found anything about that.

Take a read about vapor compression cycles used in refrigerators (although the large drop is mostly due to convertion from about 1/2 the refrigerant liquid into gas).

http://en.wikipedia.org/wiki/Refrigerator

Then you have some tricky stuff like vortex tubes:

vortex tube.htm

Thanks,
Jeff, you say temperature doesn't change for ideal but does for real-world gases..
Fred Garvin says "The short answer is yes. This is why liquids cool when taking a sudden expansion across a valve for example". However he may be talking of non-ideal gases or other physical pheneomena which cause a fluid to depart from a classical Bernoulli situation.

What gives an impression of temperature? Some say it is average kinetic energy, that is translational (X,Y,Z axis) motion.
Others are more restrictive and specify " RANDOM, DISORDERED translational motion of molecules"

If we take the second definition there should be a temperature drop when a fluid enters a restriction because part of its disordered movement is lost and becomes increased speed along the tube. Even for a monoatomic ideal gas considered incompressible.

rcgldr
Homework Helper
I'm wouldn't know. Incompressible fluids are problematic to me. For example, what would the pressure inside a container half filled with an incompressible fluid (the other half a vacuum) be in an environment without gravity? Combine incompressible and invisicid (no viscosity), and you have magic molecules than can slide against each other in any direction, but have no gaps (else the fluid would be compressible). In a pipe with variable diameters with no taper, pressure changes in such a fluid would be instantaneous, and accelerations infinite. In general, you can create some mathematical dilemmas with ideal fluids or gases, that aren't an issue in the real world, for example there is zero drag on a solid moving through an incompressible, inviscid fluid.

I just wonder what a temperature sensor would show if it were placed in the center of a Bernoulli tapering, facing the air flow of a monoatomic ideal gas. If indeed temperature is a manifestion of only "DISORDERED XYZ translational energy", then this sensor should also show a lower temperature in the taper, like the walls of the taper.

Kind of find it hard to believe, but it may be the case.

I'm not sure this analogy is valid, but if we were sitting on a molecule when it enters a Bernoulli type restriction would we suddenly find the molecule has gone cold because its lost some of its "disordered motion" ( and gained a more uniform motion), supposing of course our body maintains a regular temperature.

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Bob, thanks for your comment but the Joule Thomson Effect concerns non-ideal gas behaviour.