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The Hydrostatic Equation - UCD
For an atmosphere in hydrostatic equilibrium, the balance of forces in the vertical requires that −δp = gρδz In the limit as δz → 0, ∂p ∂z = −gρ. This is the hydrostatic equation. The negative sign ensures that the pressure decreases with increasing height. Since ρ = 1/α, the equation can be rearranged to give gdz = −αdp 4
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