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 p, 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 $\theta \left(x\right)=\sin \left(\theta \right)=\tan \left(\theta \right)=\frac{dy}{dx}$, g is the acceleration due to gravity)

$\frac{dy}{dx}=$ $\sqrt{\frac{\rho g}{S}}\times x$

$\frac{d^{2}y}{d{x}^2}=\frac{\rho gx}{S}$

$\frac{d^{2}y}{d{x}^2}=\frac{\rho g}{S}y$

$\frac{d^{2}y}{d{x}^2}$= $$ $\sqrt{\frac{\rho g}{S}}$