Past exam of the advanced fluid dynamics course of the University of Oxford 2023 2 b Solution 2026-10-25
Use the force flux at infinity in Stokes flow. With an outward normal from a large sphere, the force on the body is . Let . The leading far-field velocity and pressure areTheir rate-of-strain tensor isIn the Newtonian fluid stress tensor , the isotropic pieces cancel. Consequently,The second spherical moment integral follows from rotational symmetry and . Since , taking gives the Stokes drag law:The omitted dipole contributes a surface integral of order and vanishes in this limit. The sign refers to the fluid's drag on the moving sphere.