clau asked in Science & MathematicsPhysics · 2 years ago

# Finding height of container through the density of liquids?

The container is filled with equal masses of water and oil. The oil floats on top of water (density 1000 kg/m3), and the open surface of the oil is at a height h above the bottom of the container. What is the height h if the pressure at the bottom of the water is 400 kPa greater than the pressure at the top of the oil? Assume the oil density is 600 kg/m3. The height = hoil + hwater.

Hint: Express the volumes of oil and water in cylinder in order to get the relationship between the height of the fluid and its density. Note that density = mass / Volume. Remember m of oil = m of water.

Relevance
• NCS
Lv 7
2 years ago

"equal masses of oil and water" is the key here.

The mass of each is equal to its density * height * area

and since the area is the same for both, we infer that

ρ_oil * h_oil = ρ_water * h_water

So forget about the "2r" -- it's a distraction.

600 * h_oil = 1000 * h_water

h_water = 0.6*h_oil

We know the gauge pressure at the bottom:

P = g * (ρ_oil * h_oil + ρ_water * h_water)

substitute for densities and h_water:

400000 Pa = 9.8m/s² * (h_oil * 600kg/m³ + 0.6*h_oil * 1000kg/m³)

which solves to

h_oil = 34 m

and so

h_water = 0.6 * 34m = 20.4 m

and so

h = 54 m