Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

When I walk my kid sometimes I put a cut of coffee in a cupholder attached to the stroller. When I push the stroller over a brick pavement it seems to vibrate vertically. That is enough for the coffee to spill, even if the cup is only 3/4 full. It looked like waves were forming in the cup, beating its forward and backward sides, and they quickly grew large enough to spill.

Thus the question: is it possible to quantitively estimate the size of the waves caused by the vibration, so that one could figure out the level one can safely fill the cup to?

share|cite|improve this question
Have you tried different speeds? I ask because it could provide a hint. If changing speeds helps it may well be a resonance effect. – dmckee Jul 20 '14 at 3:14
You could always get a cup with a lid. – LDC3 Jul 20 '14 at 3:15
@LDC3: The cup did have a lid; the coffee spilled through the sipping hole. Regardless of that, I am curious about the physics related to the waves that form inside the cup, even if the answer wouldn't have a practical application. – Michael Jul 20 '14 at 3:34
@dmckee: I did; the spillage occurs even at slow stroller speed. I think it has to do with the hardness of vertical movement, such as a momentary acceleration on the order of g when passing the seem between the bricks, more than the frequency of those vertical movements, and only their frequency depends on stroller speed. – Michael Jul 20 '14 at 3:37
up vote 3 down vote accepted

Not a complete answer, but this is a classic "sloshing" problem.

The interaction between the fluid and the container wall, under the influence of the external (periodic) force sets up a (self-reinforcing) and harmful resonance.

This is of immense practical interest: jet-fuel sloshing inside airplane tanks, for instance.

share|cite|improve this answer
Thanks! I knew an effect like that had to have a name! Where would I look for references on quantitative analysis of the effect? Something like the dependency of the resonance frequency on the cylinder diameter, things like that? – Michael Jul 20 '14 at 6:15
@Michael: IANAE, but sloshing is a highly nonlinear problem (consider that the fluid can detach and form new surfaces, among other sources of nonlinearities). I know people have used Computational Fluid Dynamics (CFD) for this, but plain-vanilla CFD works only if you assume that the tank is rigid. The general problem with a deformable tank is an FSI (fluid-structure interaction) problem, which is a different beast altogether. You might wish to google "CFD + tank + sloshing" for refs. – user_of_math Jul 20 '14 at 6:27

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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