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.

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  • NCS
    Lv 7
    2 years ago
    Favorite Answer

    "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

    If you find this helpful, please award Best Answer!

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