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Old Mar 9th 2009, 11:29 PM   #1
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Unhappy Question on Fluids and Pressure

A hydrometer floats in water with 6.0cm of its stem above the water level, and in oil of density 0.8gcm^-3 with 4.0 cm of its stem above the oil level. What is the length of the stem above the water level when the hydrometer is placed in a liquid of density 0.9gcm^-3?
I used the weight, and height of above the water level to determine the total length of the hydrometer, then used it to solve for the height above the liquid level in the last part. and got an answer to 0.6mm of the answer, i wonder if it is calculation error or method error.
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Old Mar 10th 2009, 01:28 AM   #2
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The weight of the hydrometer = weight of vol of liquid displaced (Archimedes principle). Let m be the mass , L be the length , and A be the cross sectional area of the hydrometer. Let d1, d2 , d3 be the densities of the liquids and x1, x2, x3 be the length of the stem above the water level . We have

mg = d1(L-x1) A g = d2(L-x2) A g = d3(L-x3) A g.

Note that the area cancels out. Now plug in the values and solve.
I got L = 14 and x3 = 5.111 cm
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Old Mar 10th 2009, 01:44 AM   #3
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i got that same number, but the answer in the book is 5.17cm
do you think the book got it wrong?
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Old Mar 10th 2009, 05:31 AM   #4
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I think they have got it wrong or else have they used
density of water as slightly less than 1?
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Old Mar 10th 2009, 09:19 PM   #5
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i see ok thanks
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