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Setup: An aquarium filled with salt water. One edge of the tank has an overflow wier, a lower wall than the other walls, which water spills over as water is pumped into the tank.
Given a length of the wier, say 42 inches, and a rate of flow into the tank, say 2,000 gallons per hour, how high above the top lip of the wier will the water rise to accomodate that flow rate? Assume saltwater and standard window glass, if materials make a difference.
I went through a very crude dimensional analysis here, and I think that the height comes out to be about:
the cube root of (the flow rate*the water viscosity/the mass density*the gravitational acceleration*the length)
This was assuming laminar flow.
Plugging in numbers, I got that only about 1mm height was needed.
However, that's on the high side (large Reynold's number) for laminar flow. So take this as a very approximate first estimate.
(republished on 07/31/06)
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