Fluid Mechanics- Two liquids in a U-Bend

[ultrapowerpie]

Homework Statement

The problem- http://img87.imageshack.us/my.php?image=physics4cw0.jpg

Homework Equations

Part of the problem is, I don't know which equations to use. (See below)

The Attempt at a Solution

Ok, I'm not quite sure how to approach this problem. It would help if I knew which equation to use here.

I'm pretty sure it's something basic, but I just can't figure out. Any help would be appreciated...

 

[mgb_phys]

The pressure at the bottom of a column of a fluid = density * g * height
The pressure pushing down at an interface must equal the pressure pushing up if it is stable (ie not moving).

 

[ultrapowerpie]

So, let me see if I have this right then:

D1 *g* h1 = D2 *g2 * h2

D1 and D2 are given.

My confusion comes from finding h1. Once I have h1, I guess I can find h2, though they gave me the mass of the fluid added in this problem.

How can I use that to help solve this problem? I'm not quite sure what to do with that value.

 

[mgb_phys]

The pressure in the heavy liquid at the interface has gone up by the pressure needed to lift it h1.
This must be equal to the pressure at the bottom of the light liquid.

Another way to look at it is that the light liquid has lifted a weight equal to the extra column of heavy in the left hand side of the tube.

 

[ultrapowerpie]

Ok, let me approach it this way:

Since I have the mass of the liquid, I can calculate the volume it displaces. From this, using geometry, I can determine how high the dispacement is, equaling h2.

From this, can I plug it into the above formula, and come to the right answer?