Shape of surface

Classical Mechanics Level 4

Consider a large container filled with water. Let the surface tension of water be T 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 θ = sin ⁡ θ = tan ⁡ θ \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 P .
  3. The lowest point on the surface is the origin
y = P x 2 T y=\frac{Px^{2}}{T} y = T P ( cosh ⁡ P x T − cos ⁡ P x T ) y=\frac{T}{P}(\cosh\frac{Px}{T}-\cos\frac{Px}{T}) y = T P ( 1 − cos ⁡ P x T ) y=\frac{T}{P}(1-\cos\frac{Px}{T}) y = T P ( cosh ⁡ P x T − 1 ) y=\frac{T}{P}(\cosh\frac{Px}{T}-1)

Nachiket Karve by Nachiket Karve , 23, India

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