Equilibrium Levels of Mercury and Water

[LostInScience]

Homework Statement

You have a "U-shaped" container with a valve at the bottom of a negligible volume tube. The left side is filled with water and the right side is filled with mercury. The valve is opened and since the two are immiscible there is a fluid level differentiation. Determine the fluid level (distance from the bottom of the container) if the initial heights of both fluids are 1.00 meters.

Homework Equations

The Attempt at a Solution

I'm not sure how much "research I hsould be doing online to find out densities and such or if I even need them for this equation. But I found the density of water is 1.000kg/meters^3 and mercury's density is 13.6x10^3kg/meters^3

I looked up this formula in my book hoping it might help me. Pressure 2 = Pressure 1 + (Density)(Gravity)(Height). So am I correct in assuming that the pressure of water equals mercury's pressure + mercury's density x gravity x 1.00 meters?

If so, then I calculated the pressure of the water to be 133280? If that's right how do I make the jump from knowing the water's equilibrium pressure to finding out the height of the water?

I know that it's going to be higher than the mercury but how much higher?

Thank you for any help you can give me!

 

[Astronuc]

The weights of the columns of both sides much equilibrate. The mecury height decreases by h and the water side increases by h assuming constant cross-sectional area and incompressible fluid.

1 cm of Hg and the mass of 13.6 cm of water for the same cross-sectional area. Conversely 1 m of water has the same mass/weight at 0.07353 m of Hg.

 

[ogb p]

I would approach this problem by first understanding the concept of equilibrium and how it applies to fluids. In this case, the two fluids (water and mercury) are in equilibrium when the pressure at the bottom of the container is equal for both fluids. This means that the pressure at the bottom of the container must be the same for both the water and the mercury.

Using the formula you mentioned, Pressure 2 = Pressure 1 + (Density)(Gravity)(Height), we can calculate the pressure at the bottom of the container for both fluids. Since the pressure at the bottom is the same for both fluids, we can set these two equations equal to each other and solve for the height of the water.

Pressure of water = Pressure of mercury
(Density of water)(Gravity)(Height of water) = (Density of mercury)(Gravity)(Height of mercury)

Since we know the densities and gravity, we can rearrange this equation to solve for the height of the water:

Height of water = (Density of mercury/Density of water)(Height of mercury)

Plugging in the values given in the problem, we get:

Height of water = (13.6x10^3 kg/m^3 / 1.000 kg/m^3)(1.00 meters) = 13.6 meters

This means that the height of the water will be 13.6 meters higher than the height of the mercury in the container. This makes sense because the density of mercury is much higher than water, so the water needs to be significantly higher in order to have the same pressure at the bottom of the container.

In summary, to find the equilibrium level of the water in the "U-shaped" container, we need to understand the concept of equilibrium and use the formula for pressure to set the pressures of both fluids equal to each other and solve for the height of the water.