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…

Consider a water tank shown in the figure. It has one wall at $\displaystyle x=L$ and can be taken to be very wide in the $\displaystyle z$ direction. When filled with a liquid of surface tension $\displaystyle S$ and density $\displaystyle \rho$, the liquid surface makes angle $\displaystyle \theta_{\mathrm{O}}\left(\theta_{\mathrm{O}} \ll 1\right)$ with the $\displaystyle x$-axis at $\displaystyle x=L$. If $\displaystyle y(x)$ is the height of the surface then the equation for $\displaystyle y(x)$ is : (take $\displaystyle \theta(x)=\sin \theta(x)=\tan \theta(x)=\frac{d y}{d x}$, g is the acceleration due to gravity)