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So I have a tube of wrapping paper. It's at least a couple of feet long and maybe two inches wide. If I press one end of the tube firmly against my mouth and blow, I barely feel warm air come out the other end. If instead I hold the tube about half an inch to an inch away from my mouth and blow into it, I feel a good flow of air come out of the other end.

My question is why is there a difference? In both cases I would expect that since air is going in one end, it would come out the other. When I press the tube against my mouth and blow, but very little air comes out the other end, where does the rest of it go?

PS: I don't know what tags to give this question and I can't think of a good question title. I'm new to the physics sub.

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  • $\begingroup$ Strange. I don't think the air goes anywhere else in the end to mouth situation. Perhaps when blowing into the tube that is one inch away you set up a little flow pattern that takes in some of the outside air along with what you are pushing out of your mouth. How do you know there is more air in the second case? $\endgroup$ – George Herold Sep 12 '14 at 18:20
  • $\begingroup$ "How do you know there is more air in the second case?" I just mean that when I hold my hand near the other end of the tube, it feels like the amount of air that is coming out is equal to the amount that I'm exhaling. $\endgroup$ – user2023861 Sep 12 '14 at 18:25
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Very interesting observation. I think what you are observing when your mouth is away from the tube is MORE than just the air you exhale - because the air in the vicinity of your breath is being "dragged along" by something called "entrainment". This is the principle behind an ingenious fan, called the Dyson Air Multiplier:

enter image description here

A detailed explanation of how it works can be found here but it should be pretty obvious from the picture: a little bit of high speed air is being forced through holes in the rim of the "fanless" device (actually there is a fan in the base where the dark blue arrow points - it is responsible for creating the high speed jet of air) and this fast air drags a lot of slower air with it.

It's cute, and it does work. And that's what you are doing with your mouth.

The reason for the entrainment is Bernoulli's principle: when air goes faster, it has a lower pressure so it "sucks" on the air around it. When the slower molecules collide with the faster ones, they end up sharing the momentum. Instead of one fast one, you have two medium-speed ones now.

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  • $\begingroup$ I wonder if there isn't also more momentum in the entrainment case. One could imagine the entrainment leading to a higher impedance so to speak, so the OP unconsciously blows harder. $\endgroup$ – user10851 Sep 12 '14 at 18:36
  • $\begingroup$ @ChrisWhite - I don't want to rule it out, but I don't believe it's necessary to explain the observation. $\endgroup$ – Floris Sep 12 '14 at 19:10
  • $\begingroup$ When I hold the tube right against my mouth and blow, does that increase pressure in the tube? $\endgroup$ – user2023861 Sep 12 '14 at 19:33
  • $\begingroup$ @user2023861 - yes, but only very very slightly: the tube has quite a large diameter and pressure drop (for a certain volume flow rate) decreases with the fourth power of radius. If anything, when you blow from a distance you will pout your lips which will create less air blowing faster vs more air moving more slowly - just like in the Dyson Air Multiplier. $\endgroup$ – Floris Sep 12 '14 at 19:39
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As mentioned in the other answer, additional air is being entrained. This principle can be used to produce considerable flows and considerable pressure differences.

Examples

In a steam locomotive, the exhaust steam from the cylinders is directed to a nozzle that points upwards towards the exit of the funnel. This draws the smoke through the boiler and blows it out of the funnel, enabling fresh air to be drawn in for combustion. http://en.wikipedia.org/wiki/Blastpipe

Another device used in steam engines is the injector, which uses steam from the boiler to pump boiler feedwater (somewhat counterintuitively, the pressure achievable is greater than the pressure of the steam used!) http://en.wikipedia.org/wiki/Injector

In chemistry labs, a similar device uses the velocity of tap water to produce a vacuum inside dessicators (in order to dry samples) and for filtration

In industry, steam ejectors are used to maintain a vacuum, for example in the condenser of a power station boiler (there is a chance that a small amount of noncondensable gas can leak into the system.)

Carburettors use this principle to mix air and fuel. The greater the air flow, the lower the pressure, and the more fuel is sucked in. http://en.wikipedia.org/wiki/Carburetor

These devices are called ejectors, eductors,or (somewhat unspecifically) venturi devices.

Underlying physics

The principle at work here is conservation of momentum. Mechanical energy, however, is not necessarily conserved. Properly designed, long venturis can achieve reasonable efficiencies, but many devices that work on this principle do not need to be particularly efficient, and much of the mechanical energy is dissipated as heat by friction.

The Dyson Air multiplier mentioned in the other answer looks cool and is noticeably quieter than other fans (I have seen one working on display in a department store). But it is not efficient. It accelerates a small mass of air to a high velocity, then mixes it with ambient air to produce a large mass of air at low velocity.

Conservation of momentum: m1*v1 + m2*v2 = total m * combined v

When calculating the kinetic energies for the streams, it becomes apparent that unless the device is designed to ensure the velocities of the two streams are about the same at the mixing point, a lot of kinetic energy m*v^2 / 2 is wasted.

Bernoulli's principle can be used for calculations where the entrained flow is very small relative to the main flow.

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  • $\begingroup$ This is also the principle between a "no moving parts" (well, solid parts) pump available in many hardware stores. Hook it to input and output garden hoses, drop it into whatever water you want to remove, and turn on the water to the input side. It contains a nozzle which shoots a jet of water under pressure across a gap and into a larger hole, and in doing so it drags any fluid in that gap along with it. Works surprisingly well. No local fuel or electricity needed; it's "powered" by the water company's pumps. Does waste the water for the jet, of course; not great in real emergencies. $\endgroup$ – keshlam Sep 13 '14 at 0:51

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