# Bernoulli's problem (fluids)

1. Mar 30, 2008

### jrrodri7

1. The problem statement, all variables and given/known data

A simple U-tube that is open on both ends is partially filled with a liquid of density (491 kg/m^3). Water is then poured into one arm of the tube, forming a column height of (8.2 cm). The density of the heavy liquid is (1000 kg/m^3). What's the difference , h, in the height's of the two liquids?

2. Relevant equations

I'm guessing the relevant equations are directly to bernoulli's equation.
P + (1/2)$$\rho$$$$\upsilon$$^2 + $$\rho$$gy
P_1 - P_2 = $$\rho$$g(y_1 - y_2) = $$\rho$$gh

3. The attempt at a solution

I figured two equations, two uknowns....but I have no idea really. it's not really the sum of the forces, it'd have to be a pressures setup...??? help?

2. Mar 30, 2008

### Kaleb

I dont think Bernoullis principle is the correct one because it states that: When the speed of a fluid increases, internal pressure in the fluid decreases. You are trying to figure out the difference in height, not how fast the water is moving and the pressure it is exerting.

Remember that the heavy substance will replace the lighter substance. The starting state for the partially filled U-tube is x. The ending state is 8.2cm. So there is your delta distance. Try setting two equations equal to one another then solve for x.

I appologize if this doesn't help.

3. Mar 30, 2008

### Dr. Jekyll

Not in this case. Try with hydrostatic pressure ($$p=\rho g h$$). Sum of hydrostatic pressures in both arms of the tube (relative to any point) must be equal. This leads you to a simple equation.

4. Mar 30, 2008

### jrrodri7

Oh, make it static, maybe....A1v1 - a2v2 for continuity as well?

5. Mar 30, 2008

### jrrodri7

oh nevermind, the density's are different.

6. Mar 30, 2008

### jrrodri7

I'm arriving at something along the lines of p_1*g*h_1 = p_2*g*h_2 because of the differences in density and solved for h_1. Making sure it's all consistent obviously.