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If an inflated balloon is punctured, it can fly around wildly like in this cartoon @18:07.

Why is this motion so chaotic as opposed to being like a straight line or parabola as with rockets? Is there a mathematical framework for understanding why the balloon performs so much twisting and turning?

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    $\begingroup$ big question is 'would it fly straight in vacuum?' $\endgroup$
    – Alex
    May 29 '18 at 10:14
  • $\begingroup$ Without doing any sort of investigation, I would expect that the 'flapping' motion of the exhaust port, as it were, would cause it to change direction. $\endgroup$
    – Kyle Kanos
    May 29 '18 at 10:18
  • $\begingroup$ yes, although I would suspect it would average out if the flapping if much greater than the balloon speed (which is often the case). IMO, it's a combination between the flapping of the exhaust and the turbulent flow around the balloon as it moves forward. To be sure, one would have to run the experiment in near vacuum. $\endgroup$
    – Alex
    May 29 '18 at 10:32
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    $\begingroup$ Possible duplicate of Why does a balloon spiral in air instead of moving in a straight line? $\endgroup$ May 29 '18 at 10:35
  • $\begingroup$ @Alex, Yes. Take a look at the answers to the question this one is a duplicate of. $\endgroup$
    – stafusa
    May 29 '18 at 12:56
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The balloon moves because of conservation of momentum. When the gas molecules diffuse out to conserve momentum the balloon moves. But inside the balloon the gas molecules possess random motion called Brownian Motion . Suppose at time t those molecules escape in some direction. Thus conserving momentum in that direction balloon moves in opposite direction. But after very small interval dt the direction of molecules escaping out changes due to Brownian motion. Thus there is no fixed direction in which balloon would move. Hence its path is chaotic as you say.

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    $\begingroup$ brownian motion is of little consequences in this problem. If anything, there's a rotational symmetry, so it plays little role in the chaotic behaviour. $\endgroup$
    – Alex
    May 29 '18 at 10:15
  • $\begingroup$ Then there are many other factors. For example Fluid Mechanics can explain it. When gas molecules escape with some velocity through the space around that hole pressure around that face of balloon decreases according to Bernoulli's eqn: P+dgh+0.5dv^2 =constant. Thus air moves from high to low pressure taking the balloon with it $\endgroup$
    – Harshdeep
    May 29 '18 at 10:25

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