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Another hour-glass (Posted on 2010-03-15) Difficulty: 3 of 5
What is the shape of an hour-glass with the following characteristics:
1)it will be used with water, not sand
2)two identical glass shapes are fused with a tiny hole connecting them and adequate venting to prevent any changes in air pressure from impeding water flow
3)the rate of flow through the hole between the top and bottom portion is proportional to water pressure
4)the horizontal cross section of the hourglass is a circle at every level, and it is symmetric around a vertical axis
5)the water level is proportional to the time elapsed

No Solution Yet Submitted by Larry    
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Problem with question | Comment 2 of 3 |

Rule 3 states that the flow rate is proportional to the water pressure, thus denoting a linear relationship between height annd volumetric flow.  Thus, the hour glass would have a cylindrical shape at the bottom where the water is collected after passing through the hole.<p>In actual terms, the volumetric flow (velocity x cross sectional area of hole) is proportional to the square root of the pressure by this equation:

v = (2gh)

velocity equals the square root of (2 x 9.8 m/s x height in meters) 

  Posted by hoodat on 2010-03-16 01:24:56
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