I hope someone can help with this - its been driving me mad for a while now!//<![CDATA[ aax_getad_mpb({ "slot_uuid":"f485bc30-20f5-4c34-b261-5f2d6f6142cb" }); //]]>

You will have noticed the shape coffee (or whatever liquid) takes when you stir it. Clearly a vortex getting deeper and steeper the faster it is stirred.

So - here's my problem. What's the equation that defines this shape? Or, more simply, if you take a vertical slice through the centre of the vortex, what is the equation for the curve defined by the surface of the liquid? In particular, how does density, stirring speed/angular velocity and depth of liquid affect the shape? To make things simple, take a cylindrical mug.

I have thought about this problem and an approach to solving it by thinking that the liquid will take a shape that minimises its total energy (kinetic and potential). Then work out the total energy of the liquid, differentiate the resulting equation to find a minimum, and see where that gets me. Don't know if that's a good way to think about it.

Any suggestions and/or solutions very welcome.

**Physics Forums - The Fusion of Science and Community**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Fancy a cuppa?

**Physics Forums - The Fusion of Science and Community**