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class03lecnotes - Class 3 Monday January 11,2010 Reading...

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Class 3, Monday, January 11,2010 Reading: 15.3 Experiment. (Done last class) If we reversed a bottle filled to the brim with water into a container also filled to the brim with water, will the water spill? 'J A: Do you have an intuitive sense about how tall the water column needs to be for hydrostatic balance to hold (assuming there is in good approximation a vacuum at the top of the bottle as illustrated in the figure above)? Reversing the water bottle while holding its opening tight until it is under water, will cause some initial re-adjustment of the liquid-system. During this process, the column of water in the bottle will drop by a small amount, leaving above it an evacuated space (let's call it a "vacuum", even though it is not a truly hard vacuum). If we want to find out whether the liquid in the container will spill, we need to check whether a pet flow of water would be possible between e.g. points 0 and 2. Precisely, we could ask, for what height of the column there would be hydrostatic balance. I 1z~,1I"()/M~c iJI4MCt.: ~ =- Po J - D I (I /s tAt "'".It:/;! -, ro ::. ~ It.. p:t;fJ IJ ; J~ h- t/ VJlr./) I. OIJ . If) r ~ => A:::: " 1(1. J Jl- :!J}. f- /0 s.b. 9.1 jf lY tpr' ~ ') h ; 10. 117 m ;;:! /OfYL wdi/t- / h rcJ I. r:Lf For It >/0 YYl...- -P 12 >10 ::=:.-> .:::) for h ~/om Since in our experiment the column height is less than 10m, we should expect that the A water does not spill. In fact, why does it not rise? You can spend some more thought on this experiment. There are many questions to ask.
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/!;v.roWleHr~ Finally, this experiment leads us to another instrument for measuring pressure, because the height of the column of liquid is sensitive to the atmospheric pressure. If the pressure drops, the height drops as well. This relationship is described below. Po=p g h (also known as the barometer fonnula) Using a 10 meters tall bottle as an instrument to measure pressure is not very practical, What do we need to do, in order to deal with somewhat more manageable heights? What is a manageable height? f;'r!< Ii b!c,u" Mitt a. ~ d-r :4 7 r ~ J';f; . 1/ h -:: S-cJfftt.- -- tJ. {' tYL f) ! I _ / PI). /1) ~ ::: !. J' J t1i . I. JIYl 'D::- J n. - '). M = > 1_ I. Plj·/Of :,~1t: .t. pO ./0 1.11 :1-_ 2. 1n3 1.1' . tJ. Jfo IV ,;J(} X =) :f!!:!.2' /0 "h- tu..3 What liquid has such high density? .r h) /. PI J . /0 r;;(JL ---r- .: ~ ::: IJ,·/o Yi;/h{J U Ji . U& ./0 ,,:~ =")'~ :: 1l6tJ In m} So, the normal atmospheric pressure at sea level, l.013xlcfPa, can support in balance a column of Mercury with the height of 760 mm. The practical use of the above formula is thus enabled by the relationship between the atmospheric pressure and the height of the column of mercury in the tube, measured above the level of liquid in the larger container. An increase in the atmospheric pressure leads to a corresponding increase in the height of the column. This extra push is thus transmitted undiminished to the rest of the liquid. For every point within the liquid the pressure increases by the same amount. This is Pascal's Law. One application is the hydraulic lift, which you will be exploring in a homework problem. Taking the barometer e up to the t~p of Mt. Whitney, the height of the column of liquid will be 60% of its height at sea level.
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