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

Stokes' Law Calculator

By Bogna Haponiuk

The Stokes' law calculator is a tool for analyzing a spherical particle's motion in a falling ball viscometer. This device is just a vertical tube filled with viscous liquid. When dropped into the tube, a small particle is subject to a drag force resulting from the fluid's resistance. If you measure the velocity it has at the end of the tube, you can calculate the viscosity of the fluid. This article will explain how to use the terminal velocity equation to determine the viscosity, as well as elaborate a bit on the viscosity definition.

Viscosity definition

The viscosity of a fluid (gas or liquid) describes its resistance to shearing stresses. For example, honey, which is "thicker" than water, has a much higher viscosity and so is more resistant to shear stresses. The units of viscosity are pascal times second (Pa·s).

If you want to visualize how viscosity affects a liquid, consider a stream of water and honey flowing down the slope. Water has low viscosity, so it will move faster. The honey, on the other hand, will flow very slowly precisely because of its viscosity.

Terminal velocity equation

Flow lines past a falling particle at terminal velocity
Flow lines past a falling particle at terminal velocity, when the drag force Fd is equal to the force of gravity Fg. (Credit: Kraaiennest / CC BY-SA)

Our Stokes' law calculator finds the terminal velocity of a particle in a viscometer filled with a viscous fluid according to the following formula:

v = gd²(ρp - ρm)/(18μ)

where:

  • v is the terminal velocity of a spherical particle;
  • g is the gravitational acceleration - for Earth, equal to 9.80665 m/s²;
  • d is the particle diameter;
  • ρp is the density of the particle;
  • ρm is the density of the fluid; and
  • μ is the dynamic viscosity of the fluid.

You can use this terminal velocity calculator to find any of these values. If you need to determine the viscosity, simply input all other values in their respective boxes, and you will receive the answer!

Bogna Haponiuk