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Trying to remember a beautiful fluid dynamics problem and solution from my Uni days

  1. Aug 22, 2012 #1
    Hi folks,
    So the better part of ten years ago, I was a first year Theoretical Physics undergrad. And I remember the point at which I fell in love with the predictive power, and outright beauty, of equations – we were doing some fluid dynamics, and we were set the problem of a cylinder, full of water, which had a hole at the bottom. When you crunched the equations, as if by magic, the equation of a cone came out of the end. I remember the lecturer pointing out that this is the shape water makes as it drains, and my brain exploded a little bit. It was striking to me that the entire world can just fall out of these equations.

    Nowadays I work in science communication, and I haven’t stretched those particular theoretical physics muscles in a while. So I’m struggling to remember exactly what it is we did to this cylinder to get the equation of a cone – Navier Stokes? Bournoulli? Threw pencils at the paper until the random marks made the right equation? I’ve no recollection. My notes from that era are in my parent’s attic in another country, and googling around hasn’t worked. Does anyone know what I’m talking about? Am I remembering this correctly? Is it actually possible to get the equation of a cone from the setup I’ve described? This might be incredibly simple and obvious, but it’s been a while...

    Any help would be gratefully received!
  2. jcsd
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