Consider low-Reynolds-number flow past an infinite cylinder whose axis coincides with the z-axis. Try to repeat the analysis we used for a sphere to obtain an order-of magnitude estimate for the drag force per unit length.

You will encounter difficulty in finding a solution for v that satisfies the necessary boundary conditions at the cylinder’s surface ω̅ = a and at large radii ω̅ » a. This difficulty is called Stokes’ paradox, and the resolution to it by including inertial forces at large radii was given by Carl Wilhelm Oseen. The result for the drag force per unit length is F = −2πηV(α⁻¹− 0.87α⁻³ + . . .), where α = ln(3.703/Re_d), and Re_d = 2aV/ν is the Reynolds number computed from the cylinder’s diameter d = 2a.The logarithmic dependence on the Reynolds number and thence on the cylinder’s diameter is a warning of the subtle mixture of near-cylinder viscous flow and far-distance inertial flow that influences the drag.