Stokes’ law: overview

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:

F_d=6\pi\mu ru


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.


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