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Suppose you put wheels under a compressed air tank

compressed air tank

so that it can move horizontally to the right and to the left. Suppose there is a nozzle on the right hand side of the tank (in the picture on the backside, if you like).

If the tank is filled with high pressured air and you open the nozzle, the tank will move to the left. This is how rockets work and one can easily imagine that.

What happens when the tank is filled with a vacuum and you open the nozzle?

My first impression was, that the tank is moving to the right but someone told me, that it would be stand still. Is this true? What is an intuitive explanation for that?

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This question (albeit in a different guise) intrigued the young Feynman: en.wikipedia.org/wiki/Feynman_sprinkler –  Johannes Aug 15 '13 at 9:04
filled with vacuum sounds weird to me. Probably because in Spanish vacuum and empty are only one word, vacío, so you'd be saying in my language something like filled with emptiness. –  Francisco Presencia Aug 15 '13 at 14:53
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1 Answer

up vote 12 down vote accepted

I'd like to morph the question somewhat: what happens when a tank alternatively sucks in and expels fluid through the same nozzle?

The surprising answer is: it will move in the direction it would move if only fluid would be expelled. This phenomenon is known as Machian propulsion. Machian propulsion is utilized in so-called pop-pop (or putt-putt) boats: toy boats that deploy an ultra-simple steam engine.

Pop-pop (putt-putt) boat

Pop-pop (putt-putt) boat design

The abstract to this paper summarizes the physics:

"Many experimenters, starting with Ernst Mach in 1883, have reported that if a device alternately sucks in and then expels a surrounding fluid, it moves in the same direction as if it only expelled fluid. This surprising phenomenon, which we call "Machian propulsion," is explained by conservation of momentum: the outflow efficiently transfers momentum away from the device and into the surrounding medium, while the inflow can do so only by viscous diffusion. However, many previous theoretical discussions have focused instead on the difference in the shapes of the outflow and the inflow. Whereas the argument based on conservation is straightforward and complete, the analysis of the shapes of the flows is more subtle and requires conservation in the first place. Our discussion covers three devices that have usually been treated separately: the reverse sprinkler (also called the inverse, or Feynman sprinkler), the putt-putt boat, and the aspirating cantilever. We then briefly mention some applications of Machian propulsion, ranging from microengineering to astrophysics."

enter image description here

Pop-pop boat engine working cycle

Video on how to build a pop-pop boat: http://youtu.be/0ki9Kta8g14

The answer to the question posed above should now be clear: when sucking in air into an empty tank, the tank will briefly tremble but not show any sustained movement. This is even the case when the tank can move without friction: the air would rush in and the tank will start to move in opposite direction, however, the inflowing air will transfer its momentum to the tank, and the tank will come to a perfect stand still.

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Would the tank just tremble even if we assume there is no friction between the tank and the floor? One would think the air rushing in would push it ahead. –  udiboy Aug 15 '13 at 9:54
@Udiboy - the air would rush in, the tank will start to move in opposite direction, the inflowing air will transfer its momentum to the tank, the tank will come to a perfect stand still. –  Johannes Aug 15 '13 at 9:58
That seems correct! Thanks! –  udiboy Aug 15 '13 at 10:00
@RonaldBernard - sucking in air from behind would make a jet engine less effective. Or stated more extremely: building a 'pop-pop plane' is not a good idea... –  Johannes Aug 16 '13 at 16:20
@RonaldBernard - correct, it would be less effective for several practical reasons (e.g. due to increased frictional losses inside and outside the engine). –  Johannes Aug 18 '13 at 9:27
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