= Adverse pressure gradient
{title2=$\partial p/\partial s>0$}
Along a boundary-layer streamline directed by increasing $s$, an adverse pressure gradient is a rise in <pressure> in the direction of flow. The associated <pressure gradient force> opposes the <velocity>. In a steady inviscid outer stream the <Euler equation> gives $U\,dU/ds=-\rho^{-1}dp/ds$, so a positive gradient decelerates a positive outer velocity. Within a viscous <boundary layer> the slower fluid near the wall has less streamwise momentum and can reverse while the outer stream still moves forward. The onset of <flow separation> is therefore associated with vanishing and then reversed <wall shear stress>. A pressure rise does not by itself locate separation: the full boundary-layer solution and upstream history also matter.
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