Q:

Simple exercises about U-tubes

I want to solve some exercises involving U-tubes, like
You pour two non-mixing fluids with densities that go like 1:2 into a U-tube. The fluid is 5cm higher in one arm than in the other. Where is the seperating line?
Unfortunately, I don't know any of the formulas one can use for such exercises, all I know is that the pressures must be equal on both sides.
Can you supply me with the most common formula(s) used in this situation?

A:

If you poured just one liquid its level would be equal on both sides, now when you pour the liquid on one side, the liquid already present in the U tube rises by lets say h1 height. Lets assume the height of liquid column of the different liquid on other side is of height h2. 
We can find out that h2-h1 would be equal to 5 cm (difference in level of two liquids) now to equate pressure on both sides you can use 
h1 × d1 × g = h2 × d2 × g 
Here d1 and d2 are respective densities, remember the liquid having column of height h2 will be less dense as it stays above other liquid. 
On solving the equation you can find that h1 = 5 cm and h2 = 10 cm. The separation line would be at the bottom of the lighter liquid column ( the one of height h2)

