You come across an open container which is filled with two liquids. Since the tw

Question

You come 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 fills the lower portion of the container to a depth of 0.200 m which has a density of 1.00 × 103 kg/m3. The fluid which is floating on top of the water is 0.321 m deep. If the absolute pressure on the bottom of the container is 1.049 × 105 Pa, what is the density of the unknown fluid? The acceleration due to gravity is g = 9.81 m/s2 and atmospheric pressure is P0 = 1.013 × 105 Pa.

Explanation / Answer

Pressure due to water volume

P = d g h = 1,000 kg/m3 x 9.81 m/s2 x 0.200 m =1962 Pa

Therefore, the air pressure is

P_air = P + P_atm

= 1962 Pa + 101,300Pa

= 103262 Pa.

Pressure at bottom = 104,900Pa.

Pressure due to unknown fluid is differcence between these two pressures

= (104,900 - 103,320.86) = 1638 Pa.

Therefore, the density of unknown fluid

d = P / gh

= (1638  Pa. / 0.321 x 9.81 )= 520.69 kg/m^3.

Therefore, the density in g / CC is = 0.52069 g /cc

In three significant digits , density = 0.521 g/cc

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