Stokes’ law, which was derived in 1851 by an Irish scientist named George Stokes, describes the drag force exerted on a spherical object in a viscous fluid through the formula:
where
Fd is the frictional force (drag) acting on the surface of the object
μ is the viscosity of the fluid
r is the radius of the spherical object
u is the flow velocity of the fluid
The derivation of the equation for Stokes’ law involves the following steps:
Step 1: Derive the continuity equation in spherical coordinates for an incompressible fluid.
Step 2: Define the Stokes stream function to satisfy the continuity equation for an incompressible fluid.
Step 3: Derive the Navier-Stokes equations.
Step 4: Derive the differential equation, E2(E2ψ) = 0.
Step 5: Solve the differential equation.
Step 6: Derive the Stokes’ law equation.
