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Unformatted text preview: Chapter 33 Fluids: Pressure, Density, Archimedes’ Principle 239 33 Fluids: Pressure, Density, Archimedes’ Principle One mistake you see in solutions to submerged-object static fluid problems, is the inclusion, in the free body diagram for the problem, in addition to the buoyant force, of a pressure-times-area force typically expressed as PA F = P . This is double counting. Folks that include such a force, in addition to the buoyant force, don’t realize that the buoyant force is the net sum of all the pressure-times-area forces exerted, on the submerged object by the fluid in which it is submerged. Gases and liquids are fluids. Unlike solids, they flow. A fluid is a liquid or a gas. Pressure A fluid exerts pressure on the surface of any substance with which the fluid is in contact. Pressure is force-per-area. In the case of a fluid in contact with a flat surface over which the pressure of the fluid is constant, the magnitude of the force on that surface is the pressure times the area of the surface. Pressure has units of N/m 2 . Never say that pressure is the amount of force exerted on a certain amount of area. Pressure is not an amount of force. Even in the special case in which the pressure over the “certain amount of area” is constant, the pressure is not the amount of force. In such a case, the pressure is what you have to multiply the area by to determine the amount of force. The fact that the pressure in a fluid is 5 N/m 2 in no way implies that there is a force of 5 N acting on a square meter of surface (any more than the fact that the speedometer in your car reads 35 mph implies that you are traveling 35 miles or that you have been traveling for an hour). In fact, if you say that the pressure at a particular point underwater in a swimming pool is 15,000 N/m 2 (fifteen thousand newtons per square meter), you are not specifying any area whatsoever. What you are saying is that any infinitesimal surface element that may be exposed to the fluid at that point will experience an infinitesimal force of magnitude dF that is equal to 15,000 N/m 2 times the area d A of the surface. When we specify a pressure, we’re talking about a would-be effect on a would-be surface element. We talk about an infinitesimal area element because it is entirely possible that the pressure varies with position. If the pressure at one point in a liquid is 15,000 N/m 2 it could very well be 16,000 N/m 2 at a point that’s less than a millimeter away in one direction and 14,000 N/m 2 at a point that’s less than a millimeter away in another direction. Let’s talk about direction. Pressure itself has no direction. But the force that a fluid exerts on a surface element, because of the pressure of the fluid, does have direction. The force is perpendicular to, and toward, the surface. Isn’t that interesting? The direction of the force resulting from some pressure (let’s call that the pressure-times-area force) on a surface element is determined by the victim (the surface element) rather than the agent (the fluid). Chapter 33...
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- Fall '08