What is the difference in height between two liquids in a U-tube?

[jrrodri7]

Homework Statement

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?

Homework 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

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?

 

[Kaleb]

I don't 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.

 

[Dr. Jekyll]

I'm guessing the relevant equations are directly to bernoulli's equation.

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.

 

[jrrodri7]

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

 

[jrrodri7]

oh nevermind, the density's are different.

 

[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.