 Pressure gradient

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 $\mathrm{Pa}{\mathrm{m}}^{-1}$. 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.

A pressure gradient refers to the rate of change of pressure in a fluid (which can be a liquid or gas) over a specific distance. In simpler terms, it indicates how pressure varies from one point to another within a given space. The pressure gradient is a critical concept in various fields, including meteorology, fluid dynamics, and engineering.