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 , the liquid surface makes angle ₀ ( ₀ 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 (x)= (x)= (x)= d y d x , g . is the acceleration due to gravity)

Step-by-step solution

For the given element, (consider length d in Z direction) Net force in upward direction = Weight (S ( +d )-S ) d=m g Angle is small d y d x = g S ...(1) aligned & = d y d x Differentiating wrt x & ^2 d d x = d^2 y d x^2 ...(2) aligned Put d from (2) in (1) d take 1 , we get d^2 y d^2 = g y S Alternative Solution : aligned & P_A=P_B=P₀ & P_C=P₀- g y & P_C=P₀- S R & g y= S R & g y=S d^2 y d x^2 & d^2 y d^2 = g y S aligned R = 1+ ( dy dx )^2 ^ 3 / 2 ~d ^2 y dx ^2 dy / dx is very small aligned & R = 1 ~d ^2 y / dx ^2 &