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Prove that the average pressure of a liq...

Prove that the average pressure of a liquid (density ρ) on the walls of the container filled upto height h with liquid is `1/2 h rhog`.

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To prove that the average pressure of a liquid (density ρ) on the walls of a container filled up to height h with liquid is given by \( P_{avg} = \frac{1}{2} h \rho g \), we can follow these steps: ### Step 1: Understand the Setup Consider a vertical cylindrical container filled with a liquid to a height \( h \). The liquid has a density \( \rho \). ### Step 2: Define the Pressure at a Depth The pressure at a depth \( x \) from the surface of the liquid is given by the hydrostatic pressure formula: \[ ...
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