An open cylindrical vessel contains two immiscible liquids. A layer of water of height 2 m is at the bottom, and a layer of oil of height 3 m is on top. What is the absolute pressure at the bottom of the vessel? (Given: density of water = 1000 kg m ⁻³ , density of oil = 800 kg m ⁻³ , atmospheric pressure = 1.01 10^5 Pa, and g = 10 m/s ^2 )

Step-by-step solution

The absolute pressure at the bottom of the vessel is the sum of the atmospheric pressure and the pressure exerted by the two fluid columns. Pressure due to the oil layer: P_ oil = _ oil g h_ oil P_ oil = 800 10 3 = 24,000 Pa Pressure due to the water layer: P_ water = _ water g h_ water P_ water = 1000 10 2 = 20,000 Pa Total gauge pressure at the bottom: P_ gauge = P_ oil + P_ water = 24,000 + 20,000 = 44,000 Pa = 0.44 10^5 Pa Absolute pressure at the bottom: P_ abs = P_ atm + P_ gauge P_ abs = 1.01 10^5 + 0.44 10^