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Unformatted text preview: Class 2, Friday, January 8,2009 Reading: a. IS: 2. In last class' experiment. we've established that in a liquid, the pressure varies with height. This tells us something about the importance of gravity in contributing to the pressure in a liquid. A: If we filled the bottle with gas. would the gas also squirt out with the largest speed through the bottom hole? Imagine, we filled the bottle with air at slightly higher pressure than the atmospheric pressure. To first approximation, the gas would squirt out at the same rate through all three holes. Strictly speaking, the difference in airspeed exiting the holes is very small, because the pressure does not vary sensibly over the height of the bottle. This is because the extra weight of the air near the top of the bottle is very small in comparison to the weight of an equivalent volume of water. In a gas like air. the pressure is primarily' determined by the density and by the temperature. We say that the thermal contribution to the pressure in a gas dominat~ gravitational contribution. The difference in pressure is practically immeasurable for a container of small size. If we made our bottle as tall as Mt. Whitney (14,494 feet), the density of air on its top is 60% of the density at sea level (O.6xdensity at sea-level). Why is this? This is, because the pressure has to fall off gradually as we go to higher altitudes. This is. in tum, because the stuff lower down has to support a higher mass of overlying air against the force of gravity. For a liquid the pressure increases with depth because the overlying weight of liquid increases. This is the gravitational contribution to the pressure. There is also a thermal contribution, which depends on the temperature of the fluid, which, in turn, determines how strongly the molecules jostle each other around. For liquids, this thermal contribution is very small compared to the gravitational effect. Furthermore, attractions between the molecules themselves due to van der Waals forces can completely offset the thermal contribution. In absence of gravity, liquids have essentially zero pressure throughout the container. In the lab, you will deal with containers that have smaU enough beights so that you can assume that the pressure of gas within them is to an exceUent approximation constant. (In a container 100 m tall, the pressure at the bottom is only 1 % larger than at the top), We will verify this whole complex of statements in a bit L.I While the density of air on Mt. Whitney is 60% that on sea level, the density of water at a depth of 14,494 feet is nearly the same as on the surface. This shows again that while gas;es are highly compressible, liquids are nearly incompressible....
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- Winter '08