Fluid Mechanics of water and oil

[Jayhawk1]

Here's the question: Water and then oil are poured into a U-shaped tube, open at both ends, and do not mix. They come to equilibrium as shown in the figure below, where y oil = 26.9 cm and y water=18.6 cm. What is the density of the oil? (Take the density of water as 1000 kg/m3.)

I know that I need to use the P= Po+pgh somewhere and that where the two liquids are at equal height the pressure below that is equal... but I can't seem to get the right answer. I know it is simple- so can anyone help?

 

[FredGarvin]

The two fluids are in equilibrium. Therefore their weights must be equal and opposite. Do a simple FBD and solve for the weight of oil required to counter the weight of the water.

BTW...there was no diagram. Do you know the correct answer?

 

[thepatientmental]

The fluid mechanics of water and oil can be explained by the principles of buoyancy and density. In this scenario, the two liquids are not mixing because they have different densities. The density of a substance is defined as its mass per unit volume, and it is a key factor in determining how a fluid will behave in a given situation.

In this case, we have a U-shaped tube filled with water and oil, and they have come to equilibrium at different heights. This is because the oil, which has a lower density than water, is floating on top of the water. To calculate the density of the oil, we can use the equation P= Po+pgh, where P is the pressure at a certain height, Po is the atmospheric pressure, p is the density of the fluid, g is the acceleration due to gravity, and h is the height.

Since the two fluids are at the same pressure at the same height, we can set the pressures for both fluids equal to each other. We know that the pressure at the top of the water is equal to the pressure at the top of the oil, so we can set up the following equation:

Po + pwaterghwater = Po + poilghoil

Since the atmospheric pressure (Po) is the same for both fluids, we can cancel it out on both sides of the equation. We also know that the density of water is 1000 kg/m3, so we can substitute that in for pwater. This leaves us with the following equation:

1000 kg/m3 * ghwater = poil * ghoil

Next, we can plug in the given values for the heights of the water and oil, which are 18.6 cm and 26.9 cm respectively. We also know that the acceleration due to gravity is 9.8 m/s2, so we can convert the heights to meters and plug in all the values to solve for the density of the oil:

1000 kg/m3 * 0.186 m * 9.8 m/s2 = poil * 0.269 m * 9.8 m/s2

Solving for po, we get a density of 697.35 kg/m3 for the oil. This is significantly lower than the density of water, which makes sense as the oil is floating on top of the water. The lower density of the oil allows it to stay on top of the water, creating the equilibrium we see in