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:

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Answer :
Solution :

dθ
dx
=
d2
y
d
x2 ....... ( 2 )
from equations (1) and (2)
Sz
(
d2
y
d
x2
dx
)
=
(
dx
)
z
ρ
g
y
d2
y
d
x2
=
ρg
S
y