Stokes' Law Calculator

Stokes' law gives the drag on a small sphere moving slowly through a viscous fluid.

How the Math Works

Stokes' Law calculates the drag force exerted on a small sphere moving through a viscous fluid using the formula F = 6π·μ·r·v. Here, μ represents the fluid's viscosity (a measure of its resistance to flow), r is the sphere's radius, and v is its velocity relative to the fluid. The equation assumes laminar flow conditions and spherical objects, showing that drag force increases linearly with viscosity, radius, and velocity. This relationship is derived from balancing gravitational, buoyant, and viscous forces in slow-moving systems.

Practical Applications

Engineers and scientists use Stokes' Law to design systems involving fluid dynamics, such as settling tanks in water treatment plants, where particle sedimentation rates determine filter efficiency. It also helps in determining the terminal velocity of particles in suspensions, critical for optimizing pharmaceutical drug delivery or analyzing soil permeability. Researchers apply it in microfluidics to predict how cells or nanoparticles move through narrow channels, ensuring precise control in lab-on-a-chip devices.

Day-to-Day Use

This principle explains everyday phenomena like why raindrops fall at constant speeds or how dust settles in a room. It helps in designing everyday products such as shaken aerosol sprays, where droplet size affects dispersion, or in sports equipment like golf balls, whose dimpled surfaces reduce drag. Understanding fluid resistance also improves HVAC systems, ensuring efficient air circulation in homes and offices by calculating airflow resistance through ducts or filters.

Worked example

0.5 mm sphere at 0.02 m/s in water → about 1.88 × 10⁻⁹ N.

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