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yesterday comment added Chemomechanics A force balance on a motionless infinitesimal cube with side length $dx$ shows that the weight $\rho g (dx)^3$ must be offset by a pressure difference $dP$ acting on the top and bottom areas $(dx)^2$. So $\frac{dP}{dx}=\rho g$. Integrate this from the surface with gauge pressure $0$ to get gauge pressure $P(h)=\rho g h$ at depth $h$.
yesterday comment added Star Gazer Well thanks but i was looking for the mathematics however complex it may be. As we know the net force on the body is simply Buoyant Force - Weight, How do i derive it using calc?
yesterday comment added Allure @StarGazer how do your find the force on an object? You integrate, using calculus, It's how we treat varying numbers (e.g. kinematics with non-constant acceleration). If you've not encountered calculus before, you should within a few years.
yesterday comment added Star Gazer Thanks for the answer. Apologies for editing the question, could you also answer the other question. Thanks
yesterday history answered Allure CC BY-SA 4.0