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You come across an open container that is filled with two liquids. Since the two liquids have different densities, there is a distinct separation between them. Water, which has a density of rho w = 1.00 × 10 3 kg/m 3 , fills the lower portion of the container to a depth of 0.221 m . The fluid that is floating on top of the water is 0.335 m deep. If the absolute pressure on the bottom of the container is 1.049 × 10 5 Pa , what is the density, rho l , of the unknown fluid? The acceleration due to gravity is g = 9.81 m/s 2 and atmospheric pressure is P 0 = 1.013 × 10 5 Pa .

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boffeemadrid

Answer:

496.57492 kg/m³

Explanation:

[tex]P_a[/tex] = Atmospheric pressure = 101300 Pa

[tex]\rho_w[/tex] = Density of water = [tex]1000 kg/m^3[/tex]

[tex]h_w[/tex] = Height of water = 0.221 m

[tex]h_l[/tex] = Height of fluid = 0.335 m

g = Acceleration due to gravity = 9.81 m/s²

[tex]\rho_l[/tex] = Density of the unknown fluid

Absolute pressure at the bottom

[tex]P_{abs}=P_a+\rho_wgh_w+\rho_lgh_l\\\Rightarrow \rho_l=\frac{P_{abs}-P_a-\rho_wgh_w}{gh_l}\\\Rightarrow \rho_l=\frac{104900-101300-1000\times 9.81\times 0.221}{9.81\times 0.335}\\\Rightarrow \rho_l=435.73873\ kg/m^3[/tex]

The density of the unknown fluid is 496.57492 kg/m³

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