0
$\begingroup$

How do I quantify how much kinetic energy would be released from popping a balloon?

I believe that any additional kinetic energy that results from the balloon will come from it being pressurized, but how is that calculated?

$\endgroup$
0
$\begingroup$

There are two components to the total energy in the balloon:

1) The P*V work done on the air (or whatever fluid you've filled it with) and

2) the stress*strain work done on the rubber as the balloon expands. The latter is tricky to calculate (due to rubber's nonlinearity, large-strain modeling of the membrane, etc.)

If one starts from an uninflated balloon, all the work is done by forcing the fluid into the balloon. So you might measure the pressure and flow rate (dv/dt) -- ideally sampled simultaneously) -- from uninflated to the bursting point, and numerically integrate P * delta_Volume, from (negligible initial volume) up to the bursting volume (and pressure) of the balloon.

My guess is that consumer balloons have somewhat uneven wall thicknesses, so expect a fairly wide range of results.

| improve this answer | |
$\endgroup$
  • $\begingroup$ Interesting. If I assume, for the sake of simple calculations, that the balloon never expands (and was always at its fully inflated size), I could simply use the pressure x volume to acquire an answer in Joules? $\endgroup$ – Hypnos Stratagem Jul 8 '19 at 1:59
  • $\begingroup$ Simply multiplying the (final) pressure and (final) volume will give you an incorrect answer for 2 reasons: first, that would completely ignore the stress * strain work, but it would also get the PV work wrong, because the pressure is not constant! See ideal gas law. So you've gotta integrate P * dv from P0 up to Pfinal to get the fluid portion of the energy correct. $\endgroup$ – Catalyst Jul 8 '19 at 11:19
  • $\begingroup$ I don't see why any integration is needed. Pressure is a state function and so only the final value should matter. Perhaps I should restate how I am seeing the problem. Let's pretend that the baloon is a rigid, fixed wall sphere that does not appreciably expand. I think that the energy released from this sphere being popped should be the final pressure x volume of the container. $\endgroup$ – Hypnos Stratagem Jul 8 '19 at 16:47
  • 1
    $\begingroup$ Re the need for integration, please see a basic text on thermodynamics, specifically how to calculate the enthalpy of a control volume of gas. Your stated problem is about popping a balloon; ballons only pop if they can stretch (variable volume.) A rigid no-longer-remotely-like-a-balloon simply wouldn't pop! Would you kindly stick to your original question (elastic balloon popping) -- or else ask your new variation as separate questions the multiple changes -- in comments yet -- is not good stack exchange behavior, IMHO! $\endgroup$ – Catalyst Jul 8 '19 at 23:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.