In this how they have written the expression of $P_{ex}$

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This website explains : https://web.mst.edu/~gbert/SurfaceTension/back.htm.

The equation being quoted is the Young-Laplace Equation which relates excess pressure across a surface to the surface tension and radius of curvature. Any surface can have more than one radius of curvature. $R_1, R_2$ are the Principal Radii of Curvature in two mutually perpendicular planes. For a spherical surface $R_1=R_2$, while for a **cylindrical surface** $R_2=\infty$.

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