Flow Time in an Hourglass
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.
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
 Paul's Online Math Notes. "Calculus I - Notes." (May 15, 2015) http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx.
 Math Central. "Sand in an Hourglass." (May 14, 2015) http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/luke1.html.