Slender-body theory

Slender-body theory approximates the hydrodynamic force on a long thin body by a force density determined primarily by its local tangent and velocity, with logarithmic dependence on the aspect ratio.

At leading logarithmic order, a straight slender rod with unit tangent $\mathbf{t}$ and local velocity $\mathbf{v}$ exerts force per unit lengthwhere $C$ depends logarithmically on the rod aspect ratio.