text: The scallop theorem is a consequence of the subsequent forces applied to the organism as it swims from the surrounding fluid. For an incompressible Newtonian fluid with density  and dynamic viscosity , the flow satisfies the Navier–Stokes equations:
  where  denotes the velocity of the fluid. However, at the low Reynolds number limit, the inertial terms of the Navier-Stokes equations on the left-hand side tend to zero. This is made more apparent by nondimensionalizing the Navier–Stokes equations. By defining a characteristic velocity and length,  and , we can cast our variables to dimensionless form:
  where the dimensionless pressure is appropriately scaled for flow with significant viscous effects. Plugging these quantities into the Navier-Stokes equations gives us:
  And by rearranging terms, we arrive at a dimensionless form:
  where  is the Reynolds number. In the low Reynolds number limit (as ), the LHS tends to zero and we arrive at a dimensionless form of Stokes equations. Redimensionalizing yields: