Posted: August 10th, 2015

A cilium of length L=2µm and diameter .4µm sweeps through

A cilium of length L=2µm and diameter .4µm sweeps through extra-cellular fluid (u=1cP) with constant angular velocity, w. You can model this rotation of the cilium about its base, assuming that the cilium has the form of a rigid cylinder. The drag force exerted per unit length on a cylinder is f=k(subscript1)µU where k(subscript1) is a constant and U is the local fluid velocity passing over the cylinder.

Show that the torque Mo, exerted onthe base of the cilium by the cell body must therefore be;

Mo=(k(subscript1)µwL^3)/3 U=wr