Consider a water tank shown in the figure. It has one wall at x = L and can be taken to be very wide in the z direction. When filled with a liquid of surface tension S and density ρ, the liquid surface makes angle θ₀ (θ₀ << 1) with the x-axis at x = L. If y(x) is the height of the surface then the equation for y(x) is:

(take θ(x) = sin θ(x) = tan θ(x) =(\frac{dy}{dx}, ) g is the acceleration due to gravity)
- ((a))
(\frac{d^2 y}{dx^2} = \frac{\rho g}{S} x )
- ((b))
(\frac{d^2 y}{dx^2} = \frac{\rho g}{S} y )
- ((c))
(\frac{d^2 y}{dx^2} = \sqrt{\frac{\rho g}{S}})
- ((d))
(\frac{dy}{dx} = \sqrt{\frac{\rho g}{S}} x)
Show Answer
(\frac{d^2 y}{dx^2} = \frac{\rho g}{S} y )
Correct option is: (2) d2y/dx2 = (ρg / S) y
Explanation:


Curvature = 1 / ROC = |d2y/dx2| / (1 + (dy/dx)2)3/2 ≈ |d2y/dx2| / (1 + 0)3/2 = d2y/dx2
(dy/dx) ≈ tan θ ≈ 0 (small angle approximation)
Change in pressure, ΔP = S × curvature
ΔP = S × d2y/dx2
Also, ΔP = ρgy
⇒ ρgy = S × d2y/dx2
⇒ d2y/dx2 = (ρg / S) y














































































































































