E.1 How it work Princo 469 NOVA odel Fortin-type mercurial barometer A barometer i a kind of manometer ued to meaure atmopheric preure. It wa invented by Evangelita Torricelli, and ued by Blaie Pacal to dicover that the atmophere indeed ha preure. It operation i fairly imple: If a long tet tube, filled with mercury, i placed upide-down in a jar of mercury, the level of the mercury in the tet tube will fall a hown in Figure E.1. h mercury (Hg Figure E.1 Operating principle of a mercurial barometer. Why doe the mercury level fall? Becaue the preure of the atmophere i not high enough to puh it up higher. Torricelli likely thought the empty pace at the top of the tube wa a vacuum, but it i actually filled with mercury vapor (it i, in fact, a bubble of mercury. We can ue the hydrotatic equation to evaluate the preure of the atmophere: p p 1 g h, (E.1 where i the denity of the liquid, g i gravity, and h i the height of the liquid. The preure p 1 i approximately zero, o Equation (E.1 become E-1
p patm gh. (E. Thu the height can be ued to calculate the atmopheric preure. In fact, you may have een the height of mercury ued a a meaure of atmopheric preure in weather report. The value i typically around 30 inche of mercury (inhg or around 760 mm of mercury (mmhg. Thi i the height of mercury that would be read from a mercurial barometer. The tandard way of calculating preure with Equation (E. i to aume tandard gravity, and to aume mercury i at ome tandard temperature. Standard gravity i 9.8066 m/ (3.174 ft/. The tandard temperature for mercury i 3 ºF (0 ºC, for which the denity of mercury i 13595.1 kg/m 3 (848.714 lbm/ft 3 [Reference ]. In fact, it i tandard to tate a barometer meaurement in millimeter of mercury at 0ºC (mmhg at 0ºC. Here the tandard temperature of mercury i explicitly tated, and tandard gravity i jut implied. The problem with uing tandard gravity and the denity of mercury at 0ºC to calculate the preure i that (1 the local gravity i probably not the tandard value, and ( the barometer i probably not at 0ºC. Firt, gravity varie on the urface of the earth, mot notably becaue of the hape of the earth (a flattened phere, and the centrifugal force due to it rotation. The fact that the temperature of the barometer i not 0 ºC affect the mercury denity, and to a leer extent the mercury vapor preure, and the length of the bra cale due to thermal expanion. Thee effect will have to be corrected for when we report the meaurement; the corrected meaurement i called the Local Station Preure, and aumed tandard gravity, and mercury at 0 ºC. E. aking a eaurement The following tep are taken to read the barometer: 1. Zero the barometer: Turn the citern crew at the bottom of the citern reervoir until the mercury, a viewed through the citern gla, jut touche the white zero pointer. Thi procedure i illutrated in Figure E.. Tap the citern gla and the upper mall diameter gla barometer tube at the level of the mercury column menicu, to bring each menicu to it average height. Recheck and readjut, if neceary, the level of the mercury in the citern. citern gla zero pointer citern reervoir citern adjuting crew Figure E. Zeroing the barometer. E-
. Take a reading: Raie the vernier above the top of the mercury menicu, and then lower it very lowly, until the bottom edge appear to be jut touching the TOP of the mercury menicu, a hown in Figure E.3. To eliminate parallax, the oberver eye hould be in the ame plane a the front and back lower edge of the vernier leeve. When the vernier i properly adjuted, a white light will be viible at both ide of the mercury menicu but not the top. There will, however, be a light haze over the top of the mercury. vernier Thi read 757. mm, NOT 57. mm Figure E.3. Vernier cale on barometer. Read the barometer cale( directly adjacent to the lower edge of the movable vernier. Etimate between the line on the cale, then ue the line on the vernier cale to reolve the next digit. If you do not know how to read a vernier cale, ak the intructor.. Record the temperature: Read the temperature of the barometer uing the thermometer on the device. 3. Calculate the Local Station Preure. Thi value involve correcting for temperature and gravity. 4. (Optional Calculate the Sea Level Preure. Thi i the ea level preure that correpond to the Local Station Preure. (Thi calculation i not decribed here; ee Reference 1 for detail. E.3 Calculating the Local Station Preure The following multiplier are ued to correct the initial reading: Temperature-Correction 1 L( T T ultiplier 1 ( T Tm Gravity-Correction 3 6 gc 1.637310 co( 5.9 10 co ( ultiplier E-3
Nomenclature contant etric Englih L = coefficient of linear thermal expanion of bra 0.0000184 m/m C 0.000010 in./in. F = coef. of volume thermal expanion of mercury 0.0001818 m 3 /m 3 C 0.0001010 in. 3 /in. 3 F T = tandard temperature for mercury denity 0 C 3 F m T = tandard temperature for cale 0 C 6 F T = barometer temperature = latitude (San Lui Obipo i at 35º 17 N (Note: you may need to convert thi to radian Example E-1: Calculate the tation preure in San Lui Obipo for a reading of 76.4 mmhg. The barometer temperature i.3 ºC. Report the preure in mmhg and pacal (Pa = N/m. Solution: The reading i 76.4 mmhg @.3 ºC. To correct to the tandard mercury temperature (0 ºC, we firt compute the temperature-correction multiplier: 1 L( T T 1 ( T Tm 1 (0.0000184m / mc(.3 0 C 3 3 1 (0.0001818 / (.3 0 m m C C 0.99637 Thu the temperature-corrected reading i T corrected reading (0.99637(76.4mmHg 759.63mmHg@ 0C Note that an extra digit i being carried through the intermediate calculation. Then to correct for gravity, we calculate the gravity-correction multiplier. We need firt to convert the latitude of San Lui Obipo from degree to radian: (35 17 / 60 ( rad /180 0.6158rad Then the multiplier i gc 1.637310 1.637310 0.99907 3 3 co( 5.9 10 6 co( 0.6158 5.9 10 co ( 6 co ( 0.6158 E-4
Finally, the gravity-corrected reading i g corrected gc T corrected (0.99907(759.63mmHg@ 0C 758.9mmHg@ 0C Thu the Local Station Preure (to the correct digit i 758.9 mmhg@ 0 ºC. Now, to calculate the preure in unit of pacal (Pa, we ue Equation (E., p atm gh, where g i tandard gravity, and ρ i the denity of mercury at 0 ºC. Subtituting thee and the Local Station Preure into the above, p atm gh (13595.1kg/ m 101180.5N / m 3 (9.8066m / 1m 1N (758.9mm 1000mm 1kgm / Or, to the appropriate ignificant figure (four, ince the original meaurement wa to four ig. fig., P = 1.0110 5 Pa. Comment: The Local Station Preure we calculated i NOT the ame preure reported by local weather report. Uually, the preure reported in a city or town i the local Sea Level Preure. If we wanted to obtain thi value, we would have to correct the Local Station Preure uing the local altitude. The method for thi calculation i provided in Reference [1]. Reference [1] Intruction Booklet for ue with Princo Type ercurial Barometer, Princo Intrument, 000. [] Hala, S. and Durakiewicz, T., Temperature Dependence of the Surface Energy of ercury from 0 to 50 ºC, Journal of Phyic: Condened atter, Vol. 14, 00, pp. L735-L737. E-5