bmarc92
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Given that ##P = ρgh##, there's obviously a problem with the following derivation of fluid pressure under gravity. Can someone spot the flaw?
$$W = mgh$$
$$W = ρVgh$$
$$F \cdot dh = ρVgh$$
$$F \cdot dh = ρ(Ah)gh$$
$$F \cdot dh = ρgAh^{2}$$
$$\frac{d(F \cdot dh)}{dh} = \frac{d(ρgAh^{2})}{dh}$$
$$F = 2ρgAh$$
$$\frac{dF}{dA} = \frac{2ρgAh}{dA}$$
$$P = 2ρgh$$
$$W = mgh$$
$$W = ρVgh$$
$$F \cdot dh = ρVgh$$
$$F \cdot dh = ρ(Ah)gh$$
$$F \cdot dh = ρgAh^{2}$$
$$\frac{d(F \cdot dh)}{dh} = \frac{d(ρgAh^{2})}{dh}$$
$$F = 2ρgAh$$
$$\frac{dF}{dA} = \frac{2ρgAh}{dA}$$
$$P = 2ρgh$$
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