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Fluids mechanics

1) A cubical box, 5.00 cm on each side, is immersed in a fluid. The gauge pressure at the top surface of the box is 594 Pa and the gauge pressure on the bottom surface is 1133 Pa. What is the density of the fluid? Rta 1100 kg/m3 2) The weight of a car of mass 1.20 × 103 kg is supported equally by the four tires, which are inflated to the same gauge pressure. What gauge pressure in the tires is required so the area of contact of each tire with the road is 1.00 × 102 cm2? (1 atm = 1.01 × 105 Pa.) Rta 2.94 × 105 Pa 3) On planet X, the absolute pressure at a depth of 2.00 m below the surface of a liquid nitrogen lake is 5.00 × 105 N/m2. At a depth 5.00 m below the surface, the absolute pressure is 8.00 × 105 N/m2. The density of liquid nitrogen is 808 kg/m3. (a) What is the atmospheric pressure on planet X? (b) What is the acceleration due to gravity on planet X? Answer: (a) 3.00 × 105 N/m2 (b) 124 m/s2 4) As

shown in the figure, a container has a vertical tube, whose inner radius is 32.00 mm, connected to it at its side. An unknown liquid reaches level A in the container and level B in the tube level A being 5.0 cm higher than level B. The liquid supports a 20.0-cm high column of oil, between levels B and C, whose density is 460 kg/m3. What is the density of the unknown liquid?

Rta 1800 kg/m3 5) In

the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m3) that is 3.0 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 × 104 Pa? The density of the oil is 510 kg/m3.

Answer: 4.1 m