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Consider a fluid particle `A` of mass at position `(x,y)` <br> Forces acting on particle `A` are <br> (i) pseudo force `(m omega^2 x)` <br> (ii) weight `(mg)` <br> Net force on `A` should be perpendicular to the free surface (in equilibrium) [liquid cannot take shear stress] <br> `tan theta = (m omega^2 x)/(mg) = (omega^2 x)/(g)` <br> `(dy)/(dx) = (omega^2 x)/(g)` <br> `int_0^y dy = (omega^2)/(g) int_0^x x dx` <br> `y = (omega^2 x^2)/(2 g)` <br> At `x = r, y=(omega^2 r^2)/(g)` <br> `P = P_0 + rho gy = P_0 + (rho omega^2 r^2)/(2) = P_0 + (1)/(2) rho v^2 ("since" v = r omega)`. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/CPS_V01_C14_S01_041_S01.png" width="80%">