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I am having a problem on circular flow of fluid. On all books I have read they say

[itex]\frac{dp}{dr}[/itex]=[itex]\rho[/itex]v[itex]^{2}[/itex][itex]/r[/itex]

Which make sense by using infinitesimal square volume and take the force exert.

But if I use a circular infinitesimal volume (which is usually the case for circular things), i get a different answer because the side with greater pressure have greater area.

Why is this ?

Thank you