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If I have a free jet that is subsonic, say simply the exhaust of a hair drier (operating with no heat), how does the jet pressure vary longitudinally along its axis, as it decelerates from moving to rest? It has the same ambient pressure matching requirement at the beginning and end of the jet, yet does its deceleration affect its pressure?

Also, how would this be different in an optimally expanded rocket nozzle exhaust – supersonic but pressure matched?

[Note: reposting this in Engineering as it may be more relevant.]

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4 Answers 4

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Edit

This edit is in response to some comments claiming that the wake pressure is the same as the ambient pressure across the entire wake volume.

This is not correct. We know that in the wake, the air stream is moving faster than the stationary ambient air and gradually decelerates to zero speed with respect to the ambient air.

Let,s consider a prismatic strand of the flux of air in the wake equal to a volume of a cube one unit of the surface cross-section by a length equal to the speed of the strand per second $V_{flux}$.

By Newton's second law, we know the force this cube exerts at its end is

$$F=\frac{dP}{dt}$$ We know the mass is constant because we assumed a stationary state so $P=mV \rightarrow dp=mdV$ therefore the equation becomes $$F=m \frac{dV}{dt} =m\alpha$$ So we do have a pressure $pressure= \frac{F}{A}$ but we assumed the strand section 1 unit so the $pressure = F$

End of edit

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It depends on factors such as the pressure of downwind flow, and the shape of the nozzle. whether the stream is twisting (it will expand faster and lose pressure).

Usually in small fans, the equi-pressure contour lines are like an oblong onion layered off-center, expanding irregularly and losing energy within 10-20 times the diameter of the fan. Unless the fan is designed to blow farther, e.g has a protective slower stream keeping it centered, or a proper long vent like leaf blowers.

In airplane jets, there are published Engine ingestion and wake hazard areas. there have been examples of pavement been ripped by the pressure of the wake and cause substantial damage to the fuselage. Up to 500 meters aft engine could be dangerous.

boeing wake hazaed 1

boeing h 2

boeing h 3 e

source

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    $\begingroup$ Thanks for the detailed answer! If I put it in terms of total pressure $P_0+0.5\rho v^2$ would $P_0$ remain constant while $v$ gradually decreases, or would $P_0$ also change? $\endgroup$
    – RC_23
    Commented Oct 8, 2021 at 4:31
  • $\begingroup$ @RC_23, if you are referring to stagnation pressure, P_0 or static pressure is constant and assumed to be measured well away from the stream. $\endgroup$
    – kamran
    Commented Oct 8, 2021 at 5:41
  • $\begingroup$ My original question was referring to what is the static pressure along and across the jet, which I think I understand is the only true "pressure" in a thermodynamic sense, and the only one that can be measured by a pressure sensor (without altering the flow). $\endgroup$
    – RC_23
    Commented Oct 9, 2021 at 3:36
  • $\begingroup$ if i understand you correctly, if we read the pressure continuously along the normal axis to the fan it drops gently upstream due to semi vacuum created by the fan.. then it moves up suddenly across the disk of the fan. then it gently drops as we move along down stream. $\endgroup$
    – kamran
    Commented Oct 9, 2021 at 3:45
  • $\begingroup$ Regarding the edit - please explain where the force comes from. Isn't it just from some other cube of air that is getting entrained; one that will have exactly mitigating effects? $\endgroup$
    – Phil Sweet
    Commented Jan 26, 2023 at 4:19
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The first order assumption is that the exhaust pressure matches ambient pressure at the outlet and remains so. The latter entrainment and mixing and viscous decay all occur at ambient pressure. This is a very good approximation most of the time for a free jet with no nearby boundaries and no weird wake dynamics. The presence of boundaries can seriously effect jet wake evolution as is the case with the Coanda effect.

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Do an experiment with a pitot tube measuring the pressure profile across the outlet at different distances.

That’s what we had as a lab - along with all the calculations…

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  • $\begingroup$ Any chance you can share your results?? Unfortunately 8 don't have access to a lab at the present time $\endgroup$
    – RC_23
    Commented Oct 9, 2021 at 3:38
  • $\begingroup$ @RC_23 from a lab 30 odd years ago? Theory is simple - research. $\endgroup$
    – Solar Mike
    Commented Oct 9, 2021 at 4:11
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I have some idea about what is happening in the model. The model is considering a steady flow, because the initial velocity of the jet is the same any time. So, we have no gradient of pressure in the jet, because the jet is free. We only have a static pressure, but no gradient.

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