Stokes Drag on a Sphere
Stokes Drag on a Sphere
At low Reynolds number a sphere feels a drag set purely by viscosity — Stokes’ law, used for sedimentation and viscometry.
Stokes’ drag is F = 6π·μ·r·v. where μ is the dynamic viscosity, r the sphere radius and v the speed.
Inputs
mu := 0.001 Pa·s=1e-03 kg/m/s
r := 0.001 m=1 mm
v := 0.05 m/s=0.05 m/s
Apply Stokes’ law.
F := 6·pi·mu·r·v=9.42e-07 N
Results
Valid only for creeping flow (Reynolds number below about 1). Setting this drag equal to the net weight gives a sphere’s settling velocity.
Assumptions & limitations
- Reynolds number ≪ 1 (creeping flow).
- Rigid sphere, infinite fluid.
- Steady motion.