 Adverse pressure gradient

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 $UdU/ds=-{\rho }^{-1}dp/ds$, 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.

An adverse pressure gradient occurs when pressure increases in the direction of flow. In fluid dynamics, this situation can arise in various contexts, such as in airflow over a surface or in pipe flow. ### Key Points - **Definition**: An adverse pressure gradient is a condition in which the pressure rises along the flow path, typically causing a deceleration of the fluid flow.