Stokes' Law Calculator

Created by Krishna Nelaturu
Last updated: Nov 21, 2022

Welcome to our Stokes' law calculator! With this tool, you can determine a fluid's dynamic viscosity or the terminal velocity of a sphere dropped in a falling ball viscometer. Go through the following article to learn more about Stokes' law, including:

  • Dynamic viscosity and Stokes' law.
  • Stokes' law equation.
  • Calculating dynamic viscosity using Stoke's law.
  • Calculating terminal velocity from Stokes' law.

Dynamic viscosity

When a fluid is in motion, the molecules slide past each other. The force required to keep them moving depends on the fluid's density, temperature, and viscosity. Viscosity is a measure of a fluid's resistance to flow and shear stress. Fluids with a high viscosity, like honey, are thick and sticky. Low-viscosity fluids, like water, are thin and runny.

The viscosity of a fluid can change with temperature. When a substance is heated, the molecules move faster and have less opportunity to interact, reducing the fluid's viscosity. The opposite is also true: as fluids cool down, their viscosity increases. Our water viscosity calculator will show you how water viscosity varies with temperature. You can also learn the difference between dynamic and kinematic viscosity.

Understanding how viscosity works is essential for many industries, from manufacturing to medicine. For example, viscous fluids are used in lubricants and adhesives, while low-viscosity fluids are used in coatings and cleaning solutions. By understanding the factors that affect viscosity, scientists and engineers can develop products that are better suited for their intended purpose.

Stokes' law equation

Stokes' law is a physics principle describing objects' motion through a fluid. Named after Sir George Stokes, who first published it in 1851, Stokes law relates the drag force on an object to the fluid's viscosity.

Flow lines past a falling particle at terminal velocity
Drag force and gravity acting on a body falling through a viscous fluid. Source: Kraaiennest

We can use the law to calculate the drag force on an object as it moves through a liquid or gas. The drag force is proportional to the object's velocity and the viscosity of the fluid:

Fd=6πμRvF_d = 6 \pi \mu R v

Where:

  • FdF_d - Drag force on the body;
  • μ\mu - Dynamic viscosity of the fluid;
  • R R - Radius of the body; and
  • vv - Velocity of the fluid relative to the body.

The terminal velocity of a spherical body falling in a viscometer is the maximum velocity it can attain as it falls through the fluid. At this velocity, the drag force and the force of gravity are in equilibrium. In this Stokes' law calculator, we shall focus on calculating the terminal velocity vv and viscosity μ\mu. If you wish to calculate drag force, our drag equation calculator has you covered.

From Stokes' law, we can derive a formula for the terminal velocity of a sphere to be:

v=ρpρm18μgd2v = \frac{\rho_p - \rho_m}{18 \mu} gd^2

Where:

  • vv - Terminal velocity of the sphere;
  • ρp\rho_p - Density of the sphere;
  • ρm\rho_m - Density of the fluid;
  • μ\mu - Dynamic viscosity of the fluid;
  • gg - Acceleration due to gravity, approximately 9.80665 m/s29.80665 \text{ m/s}^2 on Earth; and
  • dd - Diameter of the sphere.

From this formula of Stokes' law for terminal velocity, we can determine the fluid's viscosity or the sphere's terminal velocity. If you wish to calculate the terminal velocity of any geometry, our terminal velocity calculator can help you!

How to use this Stokes' law calculator

On brand for Calctool, our Stokes' law calculator is straightforward to use:

  1. Enter the density of the medium (fluid).
  2. Provide the density and diameter of the sphere.
    • If you wish to calculate the terminal velocity, enter the fluid's viscosity.
    • If the fluid's viscosity is what you seek, you must provide the terminal velocity of the sphere.
  3. The calculator will determine the remaining unknown using the data provided.

You can tinker with the gravitational acceleration value if you wish. By default, our calculator uses g=9.80665 m/s2g = 9.80665 \text{ m/s}^2.

Krishna Nelaturu
v = gd²(ρp - ρm)/(18μ)
Acceleration of gravity (g)
m/s²
Medium viscosity (μ)
Pa·s
Medium density (ρ_m)
lb/cu ft
Particle density (ρ_p)
lb/cu ft
Particle diameter (d)
in
Terminal velocity (v)
ft/s
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