# Hydrostatics: U-Tube

1. Sep 19, 2011

### Darth Frodo

1. The problem statement, all variables and given/known data
A u-tube of uniform cross section with vertical limbs of height 20cm has mercury of relative density 13.6 in the bottom of it. The columns of mercury in each limb are 6.9cm high. Water is poured into one limb until it just reaches the top. Find the height of the water column.

2. Relevant equations

P = $\rho$gh

3. The attempt at a solution

Please find attached.

Please excuse the massive x. I got angry.

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• ###### DSC00213.jpg
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2. Sep 19, 2011

### ehild

Your picture is good, but I would put the reference at the bottom line.

There is 6.9 cm +x height of mercury in the left limb of the U-tube, and (6.9-x) cm height of mercury +h cm height of water in the right one. The length of both vertical limbs is 20 cm, the right limb is filled with water to the top, the height of the water column +the height of mercury is 20 cm: h+(6.9-x)=20 cm. The pressure is equal in both limbs at the reference line (the red one in my picture)..

It is said that the relative density of mercury is 13.6 - given with respect to the density of water. No need to convert the densities to kg/m3. If you do it, convert also cm to m.

Your error was that you multiplied everything when calculated the pressure in the right limb. The pressure of the water column is added to that of the mercury.

ehild

#### Attached Files:

• ###### utube.JPG
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3. Sep 19, 2011

### Darth Frodo

EXCELLENT!! Thanks very much, this is extremely helpful!!

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