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Surface force denoted fs is the force that acts across an internal or external surface element in a material body. Surface force can be decomposed into two perpendicular components: pressure and stress forces. Pressure force acts normally over an area and stress force acts tangentially over an area.

Equations for surface force
Surface force due to pressure

\( {\displaystyle f_{s}=p\cdot A\ } \)

f = Force, p = pressure, A = cross sectional area of the moving fluid

Examples
Pressure related surface force

Pressure is in \( {\displaystyle {\frac {force}{area}}=\mathrm {\frac {N}{m^{2}}} }\)
Area is a \( {\displaystyle (length)\cdot (width)=\mathrm {m\cdot m} =\mathrm {m^{2}} } \)

Given a pressure of \( {\displaystyle 5\mathrm {\frac {N}{m^{2}}} =5\mathrm {Pa} } \) and an area of \( {\displaystyle 20\mathrm {m^{2}} }\) find the surface force due to pressure.

\( {\displaystyle 5\mathrm {Pa} \cdot 20\mathrm {m^{2}} =100\mathrm {N} } \)