Starting from p=F/A and ρ=m/V, derive the pressure difference between two levels separated vertically by h in a stationary liquid. Include the surface pressure p₀ when finding the absolute pressure at depth h and explain why the container's width cancels.

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A column of area A has weight ρAhg. Equilibrium gives pA=p₀A+ρAhg, hence p−p₀=ρgh and p=p₀+ρgh. Both pressure force and fluid weight are proportional to A. Choose a vertical column of cross-section A and height h. Use V=Ah and m=ρAh. Identify bottom upward pressure force, top downward pressure force and weight. Apply pA−p₀A=ρAhg. Cancel A and state stationary/uniform-density/uniform-g assumptions.

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Starting from p=F/A and ρ=m/V, derive the pressure difference between two levels separated vertically by h in a stationary liquid. Include the surface pressure p₀ when finding the absolute pressure at depth h and explain why the container's width cancels.

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