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Solved: (a) Show that the pressure exerted by a fluid P

Chapter 5, Problem 169P

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QUESTION:

(a) Show that the pressure exerted by a fluid P (in pascals) is given by P = hdg, where h is the column of the fluid in meters, d is the density in \(\mathrm{kg} / \mathrm{m}^{3}\), and g is the acceleration due to gravity \(\left(9.81\ \mathrm{m} / \mathrm{s}^{2}\right)\). (Hint: See Appendix 2.) (b) The volume of an air bubble that starts at the bottom of a lake at \(5.24^{\circ} \mathrm{C}\) increases by a factor of 6 as it rises to the surface of water where the temperature is \(18.73^{\circ} \mathrm{C}\) and the air pressure is 0.973 atm. The density of the lake water is \(1.02\ \mathrm{g} / \mathrm{cm}^{3}\). Use the equation in (a) to determine the depth of the lake in meters.

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QUESTION:

(a) Show that the pressure exerted by a fluid P (in pascals) is given by P = hdg, where h is the column of the fluid in meters, d is the density in \(\mathrm{kg} / \mathrm{m}^{3}\), and g is the acceleration due to gravity \(\left(9.81\ \mathrm{m} / \mathrm{s}^{2}\right)\). (Hint: See Appendix 2.) (b) The volume of an air bubble that starts at the bottom of a lake at \(5.24^{\circ} \mathrm{C}\) increases by a factor of 6 as it rises to the surface of water where the temperature is \(18.73^{\circ} \mathrm{C}\) and the air pressure is 0.973 atm. The density of the lake water is \(1.02\ \mathrm{g} / \mathrm{cm}^{3}\). Use the equation in (a) to determine the depth of the lake in meters.

ANSWER:

Step 1 of 4

(a) Here we will have to show that the pressure exerted by a fluid P (in pascals) is given by

P = hdg,

where h is the column of the fluid in meters, d is the density in , and g is the acceleration due to gravity ().

 

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