# Stokes' Law

on . Posted in Fluid Dynamics

Stokes' law, abbreviated as St, is a fundamental principle in fluid dynamics that describes the motion of a small spherical particle through a viscous fluid.  It provides a relationship between the drag force experienced by the particle, its velocity, and the properties of the fluid.  The law states that the drag force acting on a small spherical particle moving through a viscous fluid is directly proportional to the velocity of the particle and the radius of the particle, and is also proportional to the viscosity of the fluid.  In simpler terms, Stokes' law states that the drag force on a small spherical particle is directly proportional to the particle's radius, velocity, and the viscosity of the fluid it is moving through.  This law holds true for particles that are small enough and have low Reynolds numbers, indicating laminar flow conditions and negligible inertial effects.

This law has important implications in various fields, such as fluid dynamics, sedimentation, particle dynamics, and the study of suspensions and colloids.  It is used to estimate the settling velocity of small particles in a fluid, determine the terminal velocity of particles in air or liquids, and understand the behavior of microscopic particles in biological systems or industrial processes.

It is important to note that Stokes' law is an approximation that assumes spherical particles and laminar flow conditions.  In practical situations with larger particles or higher flow velocities, other drag models and corrections may be necessary.

### Stokes' law formula

$$F = 6 \; \pi \; r \; n \; v$$     (Stokes' Law)

$$r = F \;/\; 6 \; \pi \; n \; v$$

$$n = F \;/\; 6 \; \pi \; r \; v$$

$$v = F \;/\; 6 \; \pi \; r \; n$$

Symbol English Metric
$$F$$ = force $$lbf$$ $$N$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = sphere radius $$ft$$ $$m$$
$$n$$ = fluid viscosity $$lbf-sec\;/\;ft^2$$ $$m\;/\;s$$
$$v$$ = sphere velocity $$ft\;/\;sec$$ $$m\;/\;s$$