= Mechanical equilibrium
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Mechanical equilibrium requires <force balance> for the mechanical displacements that are allowed. Two uniform fluids separated by a freely moving, unloaded, frictionless piston with equal face <areas> require equal <pressures>. A supported piston can sustain a <pressure> difference, and a fluid in <gravity> instead obeys <hydrostatic equilibrium>. For an upward height coordinate $z$, that balance is $dp/dz=-\rho g$, where $\rho$ is <mass density> and $g$ is the downward gravitational acceleration. Mechanical equilibrium alone does not establish <thermal equilibrium> or <chemical equilibrium>.
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