Calculate the Difference in Height of Glycerin and Alcohol

[iceman_ch]

Homework Statement

Glycerin is poured into an open U-shaped tube until the height in both sides is 20 cm. Ethyl alcohol is then poured into one arm until the height of the alcohol column is 20 cm. The two liquids do not mix.

What is the difference in height between the top surface of the glycerin and the top surface of the alcohol?

Homework Equations

The Attempt at a Solution

I'm not sure where to go with this one. I would think that they would be the same height. the answer is 7.46 cm I had to request the answer. I have a test today so I stilll need to know how to get the answer.

 

[denverdoc]

the pressures must be equal on both sides. What you failed to mention were 2 constants needed to solve this, the density of glycerin and that of ethyl alcohol, equal to 1.13 and .785 respectively.

you know that height of two columns must be 40 and that because of difference in density, one side will be all glycerin while the other the entire 20cm of EtOH and some fraction of the 20cm of glycerin. That fraction will be
20-height of glycerin. That enough help?

There may be quicker ways to solve this, but this illustrates principles correctly I believe.

 

[iceman_ch]

I still don't understand matmatically how that works out to be 7.46 shouldn't it be 20

 

[denverdoc]

let h=height of glycerin, we will ignore g as in mgh and just deal with densitys since its the same everywhere:

1.13H=(20-H)1.13+20*.785 solve for H
the other side will be what? (hint the two heights =40) The difference what? Draw a picture if needed.