Hourglass-revised
Classical Mechanics
Level
1
The first 1 second of a freshly inverted hourglass has the same volume of sand flowing through the cross-section of the orifice at the middle as the last 1 second.
(That is, the rate of flow of sand through the orifice of an hourglass remains constant throughout.)
False
True
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1 solution
Solution by Laszlo Mihaly:
The sand flow rate does not depend on the pressure of the sand above orifice. This has been known for a long time, but the latest evidence is in a paper published by M. A. Aguirre et. al: "Pressure Independence Of Granular Flow Through An Aperture". arxiv.org/abs/1005.2884 Here is their conclusion:
"In conclusion, using an experimental setup which enables to control the particle velocity independently from the other parameters of the flow, we have shown that the granular flow rate through an orifice is not controlled by the local pressure...... The flow rate is controlled by the mechanism driving the grains out of the system and by the geometry of the outlet, features which govern the exit velocity, and not by the pressure upstream."