Physics · Fluid Mechanics
Consider a water tank with one vertical wall at x = L which is very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes a small angle θ0 (θ0 << 1) with the x-axis at x = L. If y(x) is the height of the surface, then the differential equation describing the shape of the surface y(x) is given by (taking θ(x) ≈ sin θ(x) ≈ tan θ(x) = dy/dx, and g as the acceleration due to gravity):
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1dy/dx = √(ρg/S)x
- 2d2y/dx2 = √(ρg/S)
- 3d2y/dx2 = (ρg/S)y✓
- 4d2y/dx2 = (ρg/S)x
Correct answer
d2y/dx2 = (ρg/S)y
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