Wolfram Demonstrations Project

13,000+ Open Interactive Demonstrations
Powered by Notebook Technology »

Flow Time in an Hourglass

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 shows how the flow of sand in an hourglass (sand timer) changes as you vary the radius of the neck between the two cones.

Contributed by: Alexandra Baumgart and Hazuki Okuda (June 2015)
Open content licensed under CC BY-NC-SA

Snapshots

Details

The equation of the volume of the frustum of the sand in the top cone with varying height is . Solving for , the height of the sand in the top cone in terms of volume is

.

The volume varies with the square of the neck width.

Snapshot 1: the width of the neck is very small; the top of the hourglass takes 33.5103 seconds to empty

Snapshot 2: the width of the neck is very large; the top of the hourglass takes 0.930842 seconds to empty

Snapshot 3: the width of the neck is intermediate; the top of the hourglass takes 2.58567 seconds to empty

References

[1] Paul's Online Math Notes. "Calculus I - Notes." (May 15, 2015) http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx.

[2] Math Central. "Sand in an Hourglass." (May 14, 2015) http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/luke1.html.

Embed Code

Take advantage of the Wolfram Notebook Emebedder for the recommended user experience.

Related Demonstrations More by Author
Browse all topics
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.
Send