a) At one location, the absolute pressure measured at the bottom of an oil tank at a depth of 2.50 m is 120 kPa. The atmospheric pressure is 101.3 kPa.
i) Calculate the density of the oil.
(3 marks)
(ii) A wooden block is found to float in the oil. It is found that 80.0% of the wood is immersed in the oil. Calculate the density of the wooden block. (3 marks)
b) Air flows through a pipe that consists of two sections of diameters 25.0 cm and 12.0 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. The velocity of the air in the 25.0-cm section of the pipe is 12.5 m/s. You can neglect any frictional losses and potential energy change. Take the air and water density to be 1.23 and 1000 kg/m^3 respectively. Calculate the differential height h of the water columns. (5 marks)
Air
25.0 cm
12.0 cm
Air on the mountain top at an elevation of 2000 m has a density of 0.980 kg/m^3. The temperature is 280 K. The gas constant of air is 0.2870 kJ/kgK.
i) Calculate the air pressure on the mountain top. (3 marks)
ii) Taking into account the fact that air is compressible, i.e. the density varies with the pressure and temperature, determine the air pressure at sea level. The temperature is found to drop linearly as a function of the elevation according to the formula: T(h) = 280 K + 0.01h. h is the downward distance from the mountain top in meters. (7 marks)