Someone studying Stokes flow past a sphere argues as follows
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Viscous flow and dynamical similarity · Viscous flow and dynamical similarity
Fluid Dynamics, Ch Stokes flow, lubrication and viscous wetting
Problem
Someone studying Stokes flow past a sphere argues as follows. "The Stokes disturbance velocity around a sphere of radius a moving at speed U decays as 1/r far away, but the part of the disturbance that carries no long-range pressure signature is best represented by the potential-flow dipole around a sphere (met with potential flow), whose velocity decays as 1/r3. Since the pressure field is tied to this potential-like part of the solution, it too must decay too fast with distance to give a finite net force on the sphere. Therefore the whole drag F=6πμaU must be viscous shear stress, with no contribution from pressure."
((a)) Find the error in this reasoning.
((b)) Using the exact Stokes pressure field around the sphere, p(r,θ)=p∞−2r23μUacosθ (with θ measured from the direction of U), compute the net force this pressure exerts on the sphere's surface r=a, and compare it with the known split of the total drag into pressure and viscous parts.