# Height difference in liquids with different densities.

1. May 10, 2013

### zeralda21

1. The problem statement, all variables and given/known data

A container formed according to the figure, as two communicating vessels, is open. Both parts have a square cross section, with side 1.0 dm of the left part and 2.0 dm of the right. From the beginning, the container contains only water, and the two water surfaces is then at same level with each other (left image). 1 dm^3 olive oil, with a density of 917 kg/m3, is poured in the left part of the container, and wait until it settles on top of the water (right image). How big is the difference in height h?

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2. Relevant equations

F = ρVg

P = F/A=ρVg/A=ρgh

ρ = m/V

3. The attempt at a solution

Converting all information to the same units we get;

F =ρVg = 917*(0.1)^3*9.81≈ 9 N

Using not that the pressure is given by P = F/A=ρgh = 9/(0.1^2)=900=917*9.81*h
which gives h=0.1m=1dm. Wrong solution by far.

What have I actually calculated?

Last edited: May 10, 2013
2. May 10, 2013

### tia89

You actually do not need to compute the force... just consider a little trick... all the water below the olive oil in the left pipe is in equilibrium with the water in the right pipe which is at the same level. Therefore you just need to balance the pressures of the oil cylinder and the remaining water cylinder
Also think how you can get the height of the oil cylinder, and how you can express the height of the water one in terms of the unknown h and the height of the oil cylinder, so that you only have one variable...