Pressure measurement in U tube with mercury and water

[sluo]

Homework Statement

Mercury is poured into a U tube. The left arm of the tube has a cross sectional area A_1 of 10 cm^2 and the right arm has a cross sectional area A_2 of 5 cm^2. One hundred grams of water are then poured into the right arm of the tube.

A: Determine the length of the water column in the right arm of the U tube
B: Given that the density of mercury is 13.6 g/cm^3, what distance h does the mercury rise in the left arm of the U tube?

Homework Equations

ρ = mass/volume
P = P_0 + ρgh

The Attempt at a Solution

For part a, let h_w denote the height of the water column. I figured that since the density of water is 1g/cm^3, we can just do

1 * 5 * h_w = 100

Since they told us that the mass of the water is 100g. This gives us 20cm, which seems reasonable.

For part b, I'm totally stumped. The picture in the book has the original mercury level marked somewhere within the column of water (i.e. the column of water is higher than the mercury in the left arm). I don't know how to figure out how far down the water pushed the mercury in the right arm.

 

[LawrenceC]

Hint: When the U tube balances out, the pressure at the lowest point of bend due to the left column of Hg must equal the pressure due to the right column of Hg plus H2O. Pressure is density times depth.

 

[sluo]

I didn't think of that... but I'm wondering how it helps because we don't know the height of the U tube or the original height of the mercury in each arm.

 

[haruspex]

First, calculate the difference in mercury levels after the water is added.