= Pressure gradient
{title2=$\nabla p$}
The <pressure gradient> is the <vector> $\nabla p$, pointing in the direction in which <pressure> increases fastest. Its magnitude is pressure change per unit distance, with units $\mathrm{Pa\,m^{-1}}$. Across a small fluid element, larger pressure on one face than its opposite produces a net <pressure gradient force> per unit <volume> $-\nabla p$.
For $p(x)=p_0-Gx$ with $G>0$, the pressure force points along positive $x$. In a long pipe, it can balance viscous resistance and sustain steady flow. In a stationary vertical column, it instead balances <gravity>, so a nonzero <pressure gradient> does not by itself prove that fluid must move. The <Cauchy momentum equation> determines acceleration from all the forces together. Comparing pressure measurements at separated positions estimates the mean gradient over their spacing.
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