Shape of surface

Consider a large container filled with water. Let the surface tension of water be \(T\). Find the equation of the surface of the water.

Assumptions:

  1. The slope of the surface at every point is small so that the assumption \(\theta=\sin\theta=\tan\theta\) can be made.
  2. The difference in pressure just above and just below the surface is same everywhere and is \(P\).
  3. The lowest point on the surface is the origin
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