 Surface pressure

Surface pressure, in fluid-mechanical loading, is the local pressure evaluated at a boundary such as an airfoil surface. It is a scalar field $p_s(\mathbf{x},t)$ over position and time, with units of pascals. The field can vary strongly along the same body even when the surrounding free-stream conditions are fixed.

For a small surface patch with outward unit normal vector $\mathbf{n}$ pointing from the solid into the fluid, the pressure contribution to the force isIt acts normally to the surface. Tangential viscous stress is a separate contribution. Experiments commonly compare the boundary value with a reference pressure $p_{\infty }$ using the pressure coefficientwhere $q_{\infty }$ is dynamic pressure. A coefficient is dimensionless; reconstructing the pressure difference requires the reference conditions.

For an original patch example, let $p_s=99.8\mathrm{kPa}$, $p_{\infty }=100.0\mathrm{kPa}$ and $q_{\infty }=500\mathrm{Pa}$. Then $C_p=-0.4$. On a $0.010{\mathrm{m}}^2$ patch, absolute pressure gives an inward force of $998\mathrm{N}$; relative to the reference pressure, the pressure-force contribution differs by $2\mathrm{N}$ outward. A negative coefficient therefore describes a reference-relative deficit, not a negative absolute pressure.

A primary wind tunnel experiment by Robert M. Pinkerton used 54 pressure orifices in a NACA4412 model and compared measured distributions at different angles of attack with potential flow predictions. Such pressure tapping observes local boundary pressures through small openings; the distribution is reconstructed from measurements at selected positions.^[ref]

Spatial resolution of surface-pressure measurements limits what that reconstruction can establish between taps. Reference pressure, probe response and flow unsteadiness also affect the result. Surface pressure integration for airfoil lift uses the reconstructed field and surface directions to obtain an overall force; one pressure reading alone does not determine lift.