In hydrodynamics, the Perrin friction factors are multiplicative adjustments to the translational and rotational friction of a rigid spheroid, relative to the corresponding frictions in spheres of the same volume.  These friction factors were first calculated by Jean-Baptiste Perrin.
These factors pertain to spheroids (i.e., to ellipsoids of revolution), which are characterized by the axial ratio p = (a/b), defined here as the axial semiaxis a
(i.e., the semiaxis along the axis of revolution)  divided by the equatorial semiaxis b.  In prolate spheroids, the axial ratio p > 1 since the axial semiaxis is longer than the equatorial semiaxes.  Conversely, in oblate spheroids,  the axial ratio p < 1 since the axial semiaxis is shorter than the equatorial semiaxes.   Finally, in spheres, the axial ratio p = 1, since all three semiaxes are equal in length.
The formulae presented below assume "stick" (not "slip") boundary conditions, i.e., it is assumed that the velocity of the fluid is zero at the surface of the spheroid.