Two liquids are inside of a U-tube, which

[PhyIsOhSoHard]

Homework Statement

Two containers are connected with a u-tube as shown above. An steady equilibrium state is reached where oil with a density of $900\frac{kg}{m^3}$ exactly fills the left leg connected to the container with pressure $p_1$ and the other other leg is filled with water. What can you say about the pressure in the two containers?

Correct answer: $p_1>p_2$

Homework Equations

$p-p_0=Δp=\rho gh$

The Attempt at a Solution

$p_{H_2O}=1000\frac{kg}{m^3}\cdot gh$
$p_{oil}=900\frac{kg}{m^3}\cdot gh$

Since their height is the same, the only difference is the density.
However going by the two equations, water seems to have the bigger pressure but that isn't the correct answer. Apparently the oil has the bigger pressure?

 

[voko]

Because the system is steady, the pressure in the middle must be equal - otherwise the system would moving.

 

[PhyIsOhSoHard]

Because the system is steady, the pressure in the middle must be equal - otherwise the system would moving.

I'm not sure I understand what you mean.

 

[voko]

What would happen if the pressure of the oil in the middle point were higher or lower than the pressure of water there?

 

[PhyIsOhSoHard]

What would happen if the pressure of the oil in the middle point were higher or lower than the pressure of water there?

If the pressure is higher, it would push the water up, right?

 

[PhyIsOhSoHard]

So is it because the pressure of the two liquids are equal to each toerh at the bottom, there has to be an additional pressure at $p_1$ that cancels out the fact that the density (and thus pressure) of the oil is lower thus stabilizing the overall pressure at the bottom, hence $p_1>p_2$ right?

 

[voko]

Right.