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(II) In a movie, Tarzan evades his captors by hiding underwater for many minutes while breathing through a long, thin reed. Assuming the maximum pressure difference his lungs can manage and still breathe is $-85 \mathrm{mm}$ -Hg, calculate the deepest he could have been.

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$$1.2 \mathrm{m}$$

Physics 101 Mechanics

Chapter 13

Fluids

Fluid Mechanics

Rutgers, The State University of New Jersey

Simon Fraser University

Hope College

University of Sheffield

Lectures

03:45

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids.

09:49

A fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases and plasmas. Fluids display properties such as flow, pressure, and tension, which can be described with a fluid model. For example, liquids form a surface which exerts a force on other objects in contact with it, and is the basis for the forces of capillarity and cohesion. Fluids are a continuum (or "continuous" in some sense) which means that they cannot be strictly separated into separate pieces. However, there are theoretical limits to the divisibility of fluids. Fluids are in contrast to solids, which are able to sustain a shear stress with no tendency to continue deforming.

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In a movie, Tarzan evades …

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Diving, particularly SCUBA…

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By what factor would a scu…

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A scuba diver breathing no…

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So Tarzan is breathing underwater through a long thin, too that he has. Unfortunately, he could only go a certain depth before the pressure difference between the outside Uh, rather his surroundings versus the pressure within his lungs. If that pressure difference is too great, um, he can his lungs can collapse, and he'll, uh, he will not be able to live that for a deep under the water. So for the pressure difference, Delta P is going to be equal to the density of water terms, the gravity times a change in height. And then here we can say that the change of height is gonna be equal to the pressure difference divided by the density of water times grafitti, the pressure distances. The maximum pressure, um, is the maximum pressure that his lungs can withstand. And then the density would be the density of water and then grabbed the woods. Accent would just be the acceleration of acceleration on earth on the Earth's surface due to gravity. So we can actually plug this in directly, So the change in pressure is gonna be 85 millimeters of mercury. And they were going to convert this into Pascal's there are 133 Pascal's for every millimeter of mercury, and this will be divided by the density of water, 1000 kilograms per cubic meter and then most plied by 9.8 meters per second squared and out to H is gonna be equal to 1.15 meters. So even if you have a long cylindrical two tube that you can breathe through, um, you could only, um, Tarzan can only reach a depth of 1.15 meters before his lungs starts to collapse. And, um, I won't be able to take the pressure difference. So again, the final answer is 1.15 meters. That is the end of the solution. Thank you for watching.

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