(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Mercury is poured into a U-tube. The left arm has a cross-sectional area A1=.001 m and the right has A2=.0005m. One hundred grams of water are then poured into the right arm. Determine the length of the water column in the right arm of the U-tube; given the density of mercury is 13.6 g/cm^3, what distance h does the mercury rise in the left arm?

2. Relevant equations

Just volumes of cylinder and pressure variations with depth:

[tex]P=P_o + ρgh[/tex]

3. The attempt at a solution

I’m not sure how to deal with this problem. I found the height in the column fairly easily since we know the density and mass and cross sectional area, it’s pretty easy to solve for h of the water column, it is .2 meters.

I’m not sure how to set up equations to solve for the distance the mercury has risen though. I don’t know how to apply the principles of static fluids here since there are two different types of fluid.

Pressures are not equal at equal heights I presume. Both surfaces of the water and the mercury must be at the same pressure, atmospheric pressure, yet are at different heights.

However I do think the pressures at points A and B (labeled in the crude scetch) are equal because below the horizontal line I draw there is only mercury.

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# Fluid Statics in U-Tubes

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