A hydrometer is a simple device used to measure the density of a liquid (you may

Question

A hydrometer is a simple device used to measure the density of a liquid (you may have used something similar to measure the density of the antifreeze coolant in your car engine). A simple version consists of a test tube of outer diameter D with a weight on the bottom. First it is placed into pure water of known density Pw and it sinks part way. A red mark is drawn on the tube at the location of the water surface, height hw from the bottom of the tube. Next it is placed into a liquid of unknown density pu. and it sinks to a shorter distance, as sketched, height hu from the bottom of the tube: a blue mark is drawn. Without doing any calculations, is the density of the unknown liquid less than, equal to. or greater than that of water? Explain. Derive an expression for unknown density Pu as a function of the other variables, as needed. Stay in variables and show all your work.

Explanation / Answer

THE DENSITY OF UNKNOWN LIQUID IS ORE THAN THAT OF WATER SEE AS THE Hu
so LESS VOLUME OF UNKNOWN LIQUID IS REQUIRED TO COMPENSATE FOR THE WEIGHT.

2. WEIGHT=VOLUME OF WATER DISPLACED*DENSITY OF WATER
=hw*Area of tube*w (1)

WEIGHT=VOLUME OF UNKNOWN LIQUID DISPLACE*DENSITY OF UNKNOWN LIQUID=hu*u (2)

FROM 1 AND 2

hw*w=hu*u

u=hw*w/hu

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