Creeping Flow Past a Sphere

Pressure, Shear Stress and Drag Variations

Variation of the pressure filed is studied in this section. The Navier-Stokes equation under creeping motion assumption in spherical coordinate system is given as

Using the expression for the velocity components as given by Equations (15) and (16), after some algebra we find

Integrating (21) and (22), it follows that

The expression for shear stress is given by

The drag force acting on the sphere then is given by

After integration, the famous Stokes drag law follows. That is

The corresponding drag coefficient is given as

where the Reynolds number is defined as