I hope someone can help with this - its been driving me mad for a while now! 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.