Explanation Given: The pressure difference between the free surface of the oil and the bottom of the container Δ P = 10 kPa Density of oil ρ o = 875 kg/m 3 Density of water (from standard tables) ρ w = 1000 kg/m 3 Formula used: Pressure at a depth due to a column of a liquid of height h and density ρ is given by, Δ P = h ρ g If two immiscible liquids such as oil and water are poured in a container, then the pressure Δ P is the sum of the pressures exerted by both the columns of liquid. Calculation: Equal masses of water and oil are poured into a cylindrical container of area of cross section A . The height of the water column is h w and that of the oil floating on water is h o . The total height of the liquid in the container is h . h w + h o = h ........(1) This is shown in figure 1 . Figure 1 Mass of water in the container is given by the expression, m = A h w ρ w ........(2) The mass of the oil is equal to that of water and is given by the expression, m = A h o ρ o ........(3) From equations (2) and (3), A h w ρ w = A h o ρ o h w ρ w = h o ρ o ........(4) The pressure difference between the top surface of the oil and the top surface of water is written using the formula as, Δ P o = h o ρ o g ........(5) The pressure difference between the top surface of water and the bottom of the container is written as, Δ P w = h w ρ w g ........(6) The pressure difference between the open surface of the oil and the bottom of the container is equal to the sum of the pressures exerted by the oil and the water columns

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ISBN: 9781429281843

Author: Tipler

Publisher: MAC HIGHER

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Chapter 13, Problem 30P

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To Calculate: The height h of the open surface of the oil above the bottom of a cylindrical container filled with equal masses of water and oil.

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Chapter 13, Problem 29P

Chapter 13, Problem 31P

Chapter 13 Solutions

Physics for Scientists and Engineers

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