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A physicist comes across an open container which is filled with two liquids. Since the two liquids have different density, there is a distinct separation between them. Water, which has a density of 1.00 g/cm3, fills the lower portion of the container to a depth of 21.8 cm. The fluid which is floating on top of the water is 30.0 cm deep. If the absolute pressure on the bottom of the container is 104900 Pa, what is the density ???? of the unknown fluid? The acceleration due to gravity is g = 9.81 m/s^2 and atmospheric pressure is P0=101300 Pa.

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Answer:

496.57492 kg/m³

Explanation:

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

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

[tex]h_w[/tex] = Height of water = 21.8 cm

[tex]h_f[/tex] = Height of fluid = 30 cm

g = Acceleration due to gravity = 9.81 m/s²

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

Absolute pressure at the bottom

[tex]P_{abs}=P_a+\rho_wgh_w+\rho_fgh_f\\\Rightarrow \rho_f=\frac{P_{abs}-P_a-\rho_wgh_w}{gh_f}\\\Rightarrow \rho_f=\frac{104900-101300-1000\times 9.81\times 0.218}{9.81\times 0.3}\\\Rightarrow \rho_f=496.57492\ kg/m^3[/tex]

The density of the unknown fluid is 496.57492 kg/m³

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