Terminal Velocity of Falling Particles

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration calculates the terminal velocity of a spherical solid particle falling in a fluid under the force of gravity.


Three forces act on the particle: the downward force of gravity, an upward force of buoyancy, and a drag force that acts opposite to the direction of motion of the particle. The equation relating these forces to the particle acceleration is:


where is the radius of the sphere; and are the densities of the fluid and the particle, respectively; is the gravitational constant; is the particle velocity; and is the drag coefficient that varies with the Reynolds number, , as follows [1]:


where is the viscosity in and is the particle diameter; CGS units are used throughout. The equation for is valid over the entire range of the available experimental data; use beyond is not reliable. For the equation follows the creeping flow result . You can calculate the terminal velocity, the Reynolds number, and the drag coefficient over a wide range of the variables , , , , and . The artificial values of gravity included in the calculation can be achieved particularly in space, but also on Earth.


Contributed by: Clay Gruesbeck (June 2015)
Open content licensed under CC BY-NC-SA




[1] F. A. Morrison, “Data Correlation for Drag Coefficient for Sphere,” Department of Chemical Engineering, Michigan Technological University, 2013. http://www.chem.mtu.edu/~fmorriso/DataCorrelationForSphereDrag2013.pdf.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.