# The speed of air rising through a heated tube

I would like to get an explanations of an observed physical phenomena.

When a metal tube is placed vertically and heated and the air inside rises, the speed of the air moving through the tube continues to increase greatly when the tube reaches a certain temperature, despite no further increase in temperature.

I would like to understand why.

A little background:

Many years ago I was working on a construction project in the Kalahari Desert when I saw something unusual. In the works yard. There was a length of straight galvanised thin wall steel pipe standing vertically, about 15 cm dia and about 2.4 m long, that was making a very unusual noise like a jet engine. I went closer and saw that the bottom of the pipe rested on the corner of a tin box and was in the shade but the rest of the pipe was in the hot sun (45 degrees in the shade) and I was unable to touch it due to its high temperature. The noise was being generated by air that was being drawn up into the bottom of the pipe and then pushed out of the top at extremely high speed.

The only reason that I could see for this was that I was observing some sort of ram or standing wave effect and the air rising up the inside of the pipe had accelerated due to this. As the sun went down and the temperature dropped the phenomenon got less and less until it stopped. The same thing happened each day when the pipe got hot.

• Bob can you clarify a bit? Do you mean that the speed of the flowing air increases as it travels up the tube? Or do you mean that the max speed at the exiting end increases with temperature up until some threshold, past which the max exiting speed no longer changes with increasing temperature? – honeste_vivere Apr 26 '15 at 10:52
• live honestly, As the tube is heated the air in the tube rises. When the tube is hot i.e reaches a certain temperature, no further heat is added but it is maintained at a steady temperature. To start with, the temperature is increased, the air speed up the tube increases in velocity up to a certain point. The temperature is held and then the air continues to further increase in velocity by a moderate amount then no longer increase but remains steady. I am interested in airflow rate as it appears to generate a great deal of momentum and therefore power at the exit end of the pipe. – Bob Webster Apr 26 '15 at 12:47

The effect you describe is really just the "draw" of a chimney - hot air rises because it is less dense than cooler air. The weight of the column of air inside the chimney is this less than the weight of the column of air it displaced (Archimedes' principle) and it experiences an upwards force. Again, because air is light you only need a little bit of force to accelerate it.

According to the calculator found at http://engineeringtoolbox.com/natural-draught-ventilation-d_122.html , for the dimensions you gave, and assuming the air inside the tube is heated uniformly to 45 C (with an ambient of 25 C - I just picked a number) the air flow velocity would be 1.8 m/s. In itself that might not be "roaring", but I suspect that your pipe acted a bit like an organ pipe - with a lot of resonances. That resonance leads to an amplification of the sound of rushing air, and that is why the pipe made such a lot of noise.

With the dimensions given, the air inside could quickly get up to temperature. Total air flow per hour would be about 120 m3 which would require about 2.5 MJ to heat by 25 C. The area exposed to sunlight was about 1/3 of a square meter meaning it would receive a few 100 W of sunlight. And 100 W for an hour would give 3.6 MJ. The numbers add up (are of the right order of magnitude).

• Thank you Floris. I would just point out that the shade temperature was 45C but the tube temperature in full sunlight was in excess of 100C as it was far too hot to touch. With the information that you have provided I should be able to recalculate the velocity. Is there anything I should watch for whilst doing this? thanks – Bob Webster Apr 26 '15 at 20:38
• That makes sense - 45 didn't seem quite hot enough for the tube. When the tube gets to 100 C it is unlikely that the contents will heat all the way to 100 C - if you know the power of the sunlight you could iteratively solve for mass flow and temperature (the hotter the gas, the faster it flows and the more heat you need. Since the heat input from the sun is finite, there will be some equilibrium temperature where the flowing air takes away as much heat as the sun is providing). – Floris Apr 27 '15 at 0:04
• Thank you Floris. Is it your opinion that the air flow exiting the pipe would contain usable energy? This is my final question. – Bob Webster Apr 27 '15 at 5:56
• I don't think you will be able to "harvest" the energy of the air flow to do much useful work. Mechanisms like this are sometimes used to generate natural ventilation but I don't think the geometry you describe would allow more than a few 10's of watts to be extracted - enough to change a couple of cell phones at a time. – Floris Apr 27 '15 at 12:38

Okay, so perhaps the easiest approach I can think of relates to basic fluid flow.

If we ignore gravity (and other external/internal forces) for the moment, then we can describe the fluid motion as: $$\frac{d \mathbf{v}}{dt} = -\nabla P$$ where $P$ is a scalar pressure. In an ideal gas, this can be written as: $$P = \frac{3}{2} n \ k_{B} \ T$$ where $n$ = number density of the gas (i.e., number per unit volume), $k_{B}$ = Boltzmann's constant, and $T$ = thermodynamic temperature. If we assume the density is constant, then the pressure gradient arises from the temperature gradient.

Then the limiting factors will include, but probably not limited to (in no particular order): (1) small effects from gravity; (2) speed of sound [doubtful this will be an issue unless the pipe is extremely hot]; (3) viscosity of the fluid; etc.

I am inclined to think, without knowing more about the problem, that viscosity is the limiting factor here. Unless you tell me that the speed of the exiting air is approaching the speed of sound or the pipe is very long (and oriented perpendicular to the Earth's surface locally), the system can be treated as an effectively incompressible viscid fluid. In this case, you would just add on another viscous term to the fluid equation above.

Thank you very much for taking time to answer my question, I appreciate that greatly and would like to supply the background to my question

Many years ago I was working on a construction project in the Kalahari Desert when I saw something unusual. In the works yard. There was a length of straight galvanised thin wall steel pipe standing vertically, about 15 cm dia and about 2.4 m long, that was making a very unusual noise like a jet engine. I went closer and saw that the bottom of the pipe rested on the corner of a tin box and was in the shade but the rest of the pipe was in the hot sun (45 degrees in the shade) and I was unable to touch it due to its high temperature. The noise was being generated by air that was being drawn up into the bottom of the pipe and then pushed out of the top at extremely high speed.

The only reason that I could see for this was that I was observing some sort of ram or standing wave effect and the air rising up the inside of the pipe had accelerated due to this. As the sun went down and the temperature dropped the phenomenon got less and less until it stopped. The same thing happened each day when the pipe got hot.

Thank you again

Bob

• Bob - this is good information but you need to edit it into your question rather than posting it as an answer, since on this site according to policy your post will end up being deleted as "not an answer" (which it is not - but the information deserves to be preserved...) – Floris Apr 26 '15 at 17:28
• Thanks for that. I could not find any explanation of how to respond to answers.I will bear that in mind. – Bob Webster Apr 26 '15 at 18:54
• No problem! You have discovered the "comment" section - that is normally where you discuss / clarify an answer. I edited the content of this into the question for you. – Floris Apr 26 '15 at 19:12

You mentioned: the speed of the air moving through the tube continues to increase greatly when the tube reaches a certain temperature, despite no further increase in temperature.

You might have assumed that (as the sun slowly rises) at the time the pipe is fully covered in sunlight, the pipe is immediately at it's maximum temperature. This might not be so, as the tube will take time to increase it's temperature as it absorbs the sun's heat (especially if the pipe is thick), as can be shown roughly by the equation $Q_S-Q_e=mc\Delta T$ (where $Q_S$ is the heat from the sun, and $Q_e$ is the heat on the pipe absorbed by the environment and air passing through). So at the moment when it seems to have a maximum temperature it might still not be in its max temperature, which might explain why the air continues to further increase in velocity by a moderate amount then no longer increase but remains steady, which would be the point when the pipe's temperature no longer rises.

Suggestion might be to use a thermometer to observe this, to verify if there is really no further increase in temperature while the velocity still increases.