# Multi Tube and fluid pressure

1. Mar 30, 2010

### okgo

1. The problem statement, all variables and given/known data
Now two fluids are placed in the same tube (d). Both sides are open to the atmosphere without pistons. One fluid is water and the other (on top of the water in the left branch of the tube) is an oil of unknown density. l = 135mm and d = 12.3mm. What is the density of the oil?
Image here:
http://screencast.com/t/ZGEwODAy
2. Relevant equations

change in pressure=density*g*h

3. The attempt at a solution

I'm not sure how to start. I feel this is going to be the hardest topic for me to grasp

2. Mar 30, 2010

### AtticusFinch

Ok so start by looking at the picture. Look at the depth d + l. On the right side you have the atmosphere and some water pressing down at that point. On the left side you have the atmosphere and oil (more than the amount of water pressing down on the right). Therefore we expect the density of the oil to be smaller than water.

One of the principles of fluid mechanics is that the same liquid will have the same pressure at the same depth. For example, let's look at the water at depth d + l.

On the right side the pressure is this:

$$P = P_{atm} + \rho_{water}g(0.135 m)$$

On the left side the pressure is this:

$$P = P_{atm} + \rho_{oil}g(0.135 m + 0.0123 m)$$

Set the two equations equal to each other and solve for $$\rho_{oil}$$