Lecture_20

Lecture_20 - 11.3 Pressure and Depth When you dive deeper...

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11.3 Pressure and Depth When you dive deeper under the water in a swimming pool, for example, you feel ore pressure against you Why??? more pressure against you. Why??? P = F/A , and your area doesn’t change, so the force on you must change. The deeper you go, the more pressure you feel. Because you and the fluid are in a gravitational field, the fluid at greater depths must support the weight of the fluid above it. et’s take a look at a small column of fluid inside a much larger container: Let s take a look at a small column of fluid inside a much larger container: Let’s draw the FBD for the column of fluid. In the y-direction, we have a force on the top of the column due to the pressure there, P 1 . On the bottom of the column we have a rce due to the pressure there force due to the pressure there, P 2 . And, of course, we have the weight of the column, mg . The column of fluid is in equilibrium, so: = 0 y F
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= = 0 1 2 mg F F F y mg F F = 1 2 mg A P A P = 1 2 g A mg P P = 1 2 V m = ρ Ah m = Ah m = h A g Ah P P ) ( 1 2 = gh P P = 1 2 Notice the pressure at the top of the column is different than the pressure on the bottom of the column. The pressure depends on the depth and density of the fluid. Notice, it does not depend on the cross-sectional area of the column: The pressure is the same in each container of water, h p, since the depth ( h ) of each point is the same. The boxed equation above assumes the density of the fluid is constant, i.e. it does not change with depth. We call this an Incompressible Fluid. P P
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Assuming the fluid is incompressible is a good approximation for liquids, but not so for gases.
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Lecture_20 - 11.3 Pressure and Depth When you dive deeper...

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