The reciprocal theorem describes the relationship between two Stokes flows in the same geometry where inertial effects are insignificant compared to viscous effects. Consider a fluid filled region V bounded by surface S with a unit normal n ^ ^ . Suppose we have solutions to Stokes equations in the domain V possessing the form of the velocity fields u and u ′ . The velocity fields harbor corresponding stress fields σ σ and σ σ ′ respectively. Then the following equality holds: