Equilibrium Levels of Mercury and Water

[LostInScience]

Homework Statement

You have a "U-shaped" container with a valve at the bottom of a negligible volume tube. The left side is filled with water and the right side is filled with mercury. The valve is opened and since the two are immiscible there is a fluid level differentiation. Determine the fluid level (distance from the bottom of the container) if the initial heights of both fluids are 1.00 meters.

Homework Equations

The Attempt at a Solution

I'm not sure how much "research I hsould be doing online to find out densities and such or if I even need them for this equation. But I found the density of water is 1.000kg/meters^3 and mercury's density is 13.6x10^3kg/meters^3

I looked up this formula in my book hoping it might help me. Pressure 2 = Pressure 1 + (Density)(Gravity)(Height). So am I correct in assuming that the pressure of water equals mercury's pressure + mercury's density x gravity x 1.00 meters?

If so, then I calculated the pressure of the water to be 133280? If that's right how do I make the jump from knowing the water's equilibrium pressure to finding out the height of the water?

I know that it's going to be higher than the mercury but how much higher?

Thank you for any help you can give me!

 

[Astronuc]

The weights of the columns of both sides much equilibrate. The mecury height decreases by h and the water side increases by h assuming constant cross-sectional area and incompressible fluid.

1 cm of Hg and the mass of 13.6 cm of water for the same cross-sectional area. Conversely 1 m of water has the same mass/weight at 0.07353 m of Hg.