Empty a Cup with a Straw (Scripts) Publisher's description
from Joseph Kirk
If you dip a straw in a cup of water and hold your finger over the top, you can then pull the straw out and remove the amount** contained in the straw
If you dip a straw in a cup of water and hold your finger over the top, you can then pull the straw out and remove the amount** contained in the straw.
Obviously it would take an infinite number of dips to empty the cup completely, but did you ever wonder how many times would you have to repeat this process to lower the water level to some smaller amount?
This file provides an analytical solution (for any cup and straw dimensions) to this question and a simulated process that verifies the analytical equation, as well as a graph showing the change in water level after each dip.
** Under certain assumptions:
1. The cup and straw are perfectly cylindrical
2. The amount of water in the straw for any dip is exactly equal to the height of the water in the cup times the cross-sectional area of the straw. (Ignoring adhesive/cohesive properties of water that result in meniscus/surface tension effects)
3. The outside of the straw is completely dry at the time of removal from the cup
4. The straw has negligible volume (so its volume does not displace water in the cup when it is inserted)
System Requirements:MATLAB 7.2 (R2006a)
Program Release Status: New Release
Program Install Support: Install and Uninstall