AIR DENSITY AND ITS UNCERTAINTY. Manuel Salazar Maria Vega

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1 AIR DENSIY AND IS UNCERAINY Mnel Slzr Mri Veg

2 CONENS Air nd is comosiion Wys o clcle e ir densiy Cr CIPM Eqion Aroxime eqion Unceriny

3 Air nd is comosiion e ir is mixre of seerl gses dry ir, nd wer in sem form. roosere is e inferior lyer of e erresril mosere, erresril srfce lide of 6 o 8 kilomeers, e ir we breed is concenred ere. e dry ir s e wer sem bees like idel gses. ey e been deeloed o emiricl lws rele e mcroscoic les, in idel gses, ese les inclde ressre (), olme (V) nd emerre () Ley de Crles Ley de Gy-Lssc Ley de Boyle IDEAL GAS LAW

4 Air nd is comosiion I is consied by nirogen mixre nd of oxygen like bsic elemen (99%) nd e res like noble gses. e comosiion is similr rond e world. Wer Sem (0-5%), Crbon dioxide, ydrocrbons, rs, ses, ds nd SO. Elemeno Nirógeno Oxigeno Argón Neón Helio Crión COMPOSICION DEL AIRE PURO Proorción en olmen 78,4 0,9, ,7 0-4 Elecricl deliery form CH, H0, 03, NO3H, NH3, Hidrogeno NO3NH4. enón ,94 Proorción en eso 75,6 3, 0, ,

5 Wys o clcle e ir densiy Densiy defined in qliie mnner s e mesre of e relie mss of objecs wi consn olme Hyoesis de Aogdro wo gses sme olme (sme ressre nd emerre) conin e sme nmber of ricles, or molecles Sndrd Lw gses P.V n. R. n m/mr

6 Wys o clcle e ir densiy As fncion of lide Using refrcomeer Air boyncy refcs meods Eqion CIPM /8 Aroxime eqion

7 Wys o clcle e ir densiy AS FUNCION OF ALIUDE Amoseric ressre dros bo or bo. mbr (kp( kp) for ec 00 meers. Densiy decreses

8 Wys o clcle e ir densiy AS FUNCION OF ALIUDE L 6,5 emerre lse re, deg K/km H geooencil lide geomericl lide o emerre ºK Po Amoseric Pressre

9 Wys o clcle e ir densiy REFRACROMERY Cnges in ir densiy cn be deermined wi good recision sing n oicl meod bsed on e ig correlion beween ir densiy nd ir index of refrcion. R secific refrcion or e refrcionl inrin in ncion comosiion of ir nd e locl moseric condiions n is deermined by simle rio of lser freqencies: n ν ν cio ire ν cio lser freqency locked o one rnsmission ek of e inerferomeer nder cm ν ire e freqency locked o e sme ek of e inerferomeer lced in ir.

10 Wys o clcle e ir densiy AIR BUOYANCY AREFACS MEHODS e meod is bsed on e weiging of wo refcs ing e sme nominl mss nd e sme srfce re b wi ery differen olmes. wo weigings re necessry o deermine e ir densiy, one in ir nd one in cm m ire I I ( V V ) m m I e I blnce redings in ir mss V m e V m olme of m y m ir densiy m cío nd mss I 3 I 4 I 3 e I 4 e blnce redings in cm mss y mss m m σ S ire S S e difference in srfce re beween e wo refcs nd σ mss of dsorion er ni re. I cio 3 I 4 ( I I σ S) V m V m

11 Wys o clcle e ir densiy FORMULA CIPM From e eqion of se of non-idel gs nd e exerimenl condiions e densiy of mois ir Were M x 3 [,9635,0( x 0,0004) ]*0 8 co kgmol f (, ) s ( ) P ressre ermodynmic emerre 73,5 M molr mss of e wer comressibiliy fcor R molr gses consn

12 Wys o clcle e ir densiy APPROIMAE EQUAION From BIPM forml we obin one nmericl roxime eqion : 0,34848* 0,00904* 73,5 r * e 0,06*

13 Wys o clcle e Wys o clcle e ir densiy ir densiy PSYCHROMERY ermodynmic roeries of mixres of gs wi or.. srion ressre nd emerre of dew, Indexes of midiy, Volme, e nd mid enly, emerre of srion dibic nd we ermomeer. Some definiions: Relie Hmidiy. e relie midiy is e ercen of srion midiy,, generlly clcled in relion o sred or densiy, in (%): HR 00 P/Ps (%) emerre of dibic srion,, is e idel emerre of eqilibrim will e e ir non sred fer ndergoing n dibic nd isobric rocess (iso( enlic), i kes i emerre o e srion by mens of liqid eorion of wer o is. emerre of we ermomeer is e emerre i reces ermomeer coered wi we clo is exosed o n irflow wio sring i flows seeds ner 5 m/s Dew oin is e emerre, wic e moisre conen in e ir will sre e ir, If e ir is cooled frer, some of e moisre will condense.

merils Hygromeer of dew oin Hygromeer of Cemis bsorion

14 Wys o clcle e ir densiy o mesre e midiy : PSYCHROMERY AREFAC MEHOD sycromeer ermodynmic ygromeer of ir or oers merils Hygromeer of dew oin Hygromeer of Cemis bsorion Hygromeer digil Hygroscoic Condension Grimeric Vriion of elecricl roeries

15 Wys o clcle e ir densiy PSYCHROMERY Psycromeer nd siro sycromeer Consis wo ermomeers, one norml (dry) nd noer wi eir blb ermnenly midified nks o clo or we gze i recoers i. e midiy cn be mesred beween bo sring from e difference of emerre rses

16 Wys o clcle e ir densiy Digrm Crrier. - e reresens (ºC) in e bsciss xis (xis x) nd e mixre reson or midiy (, in kg of wer/kg of dry ir) in e xis of orderly (xis nd, o e rig). - e srion cre (HR 00%) i scends owrd e rig nd i reresens e end of e digrm. In is cre e emerres of mid ermomeer nd e emerres of dew re loced. - - e cres of midiy relie consn re similr o of srion, dncing down (lying down more) s i diminises e midiy of e ir. PSYCHROMERY

17 Wys o clcle e ir densiy CHAR ( 9, 40 %, ) 0.77 ( 0, 40 %, ) (, 40 %, ) 0.74 ( 4, 40 %, ) ( 9, 50%, ).08 ( 0, 50%, ).04 (, 50%, ) 0.96 ( 4, 50%, ) Air densiy eled wi Relie midiy 40 %, emerre 9 ºC 4 ºC, ressre 600 mbr 700 mbr Air densiy wi eled wi Relie midiy 50 %, emerre 9 ºC 4 ºC, ressre 660 mbr 000 mbr

18 Wys o clcle e ir densiy ( ) (,, 800) (,, 700) (,, 600) 0, r, r 0 r 0 r Air densiy eled wi CHAR r Relie midiy 40 % - 60 %, emerre 0 ºC, ressre 600 mbr 000 mbr 60

19 Wys o clcle e ir densiy CHAR Air densiy eled wi Relie midiy 40 %, (, 40, 000) (, 40, 800) emerre 9 ºC 5 ºC, 9 ressre 800 mbr 000 mbr 5

20 CALCULAION OF HE AIR DENSIY CIPM M R x M M Were: M R M Pressre of ir in P. molr mss of dry ir. Comressibiliy fcor Uniersl consn of idel gses emerre of ir in K molr frcion of wer sem molr mss of wer

21 Molr mss of dry ir, M If i considers consn of ir comonen M 0, kg mol - If i cn mesre e concenrion of CO M [8,9635,0 (( CO. - 0,0004)]* 0-3 kg mol -

22 Comressibiliy fcor, [ ( ) ( ) ] b b x c c x ( d ex ) Were: Air ressre in P Air emerre in K Enironmenl emerre in o C 0, K P - -,933 x 0-8 P -,043 x 0-0 K - P - b 0 5,707 x 0-6 K P - b -, P - C x 0-4 K P - C -,376 x 0-6 P - d,83 x 0-K K P - e -0,765 x 0-8 K P -

23 Uniersl Consn of idel gses, R R ± 8,4 x lo-6 6 J. mol -. K - Molr s frcion of wer sem, In fncion of relie midiy, x f (, ) s ( ) In fncion of emerre of dew oin, r s Were: s f, ) ( r f (, r ( Relie midiy Pressre of sred sem Fgciy fcor ) s r )

24 Enncemen fcor f f(, r ) f α β γ Were: α β γ, x 0-8 P - 5,6 x 0-7 K - Air ressre in P Air emerre in O C or dew oin emerre ( r ) in O C

25 Pressre of sred sem, s Px ex A s B C D Were: A, x 0-5 K- B -,9 3 6 x 0- K- C 33, D -6, x 03 K Air emerre in K or dew oin emerre (r) in K

26 UNCERAINY OF AIR DENSIY SOURCES OF UNCERAINY Amoseric emerre Clibrion of bromeric Resolion of bromeric Vriion of moseric ressre dring clibrion 3 3 U k d B B 4

27 Enironmenl condiions 3 Clibrion of ermomeer U k Resolion of insrmen d Vriion of emerre dring clibrion 3 4

28 Relie midiy of ir 3 Clibrion of ygromeer U k Resolion of ygromeer d Vriion of e ir relie midiy dring clibrion 3 4

29 Consn R of idel gses R 84x 0-7 J mol - K - Eqion djsmen for e deerminion of ir densiy ec 4 5 (x0 )(0,9495) 9,50x0 kgm 3

30 Sensiiiy Coefficien Pressre emerre Relie midiy. f f f f c P P f f P P f f c s s s s C

31 Were: ex D B A D C B A P s 8 0 3,4 P x f β f γ fp s P f x s

32 fp x s f P s ( ) [ ] ( ) ) ( ex d C C b b ( ) ( ) [ ] ( ) ex d C C b b o ( ) c b ( ) 0 e x c x c b b o

33 Consn R M M R M M M x R M M M R M M M R M M M R M R R C R molk j kgm CR 3 0,40368

34 Eqion Unceriny elion Degrees of freedom Exnded nceriny C ec ( ) [ ] i i x c ec ec R R n x ef γ k U

35 : Were : ( ) ( ) ( )( ) ()( ) s s n n r n k k k, ( ) ( ) ( )( ) ()() s s n n r n k k k, ( ) ( ) ( )( ) ( ) () s s n n r n k k k, ( ) ( ) ( ) ( ) ( ) ( ), N i N i j j i j i j i i i i x x r x x c c x c Consider e moseric ressre, emerre nd relie midiy re correled, is nceriny:

36 Reference Esimciòn de l inceridmbre en l deerminciòn de l densidd del ire, Lis Omr Becerr Snigo y mrì Elen Grddo gonzàlez,, CENAM, Abril 003. Eqion for e deerminion of e densiy of Moir Air, R.S. Dis, Merologi 99,9, Eqion for e deriminion of e densiy of mois ir,, P. gicomo.merologi 8, ree meods of deermining e densiy of mois ir dring mss comrisons,, A. Picrd y. Fng. Merologi 00, 39, Discrencies in ir densiy deerminion beween e ermodynmic forml nd grimeric meod: eidence for new le of e mole frcion of rgon in ir,, A Picrd, H. Fng, Merologi 4,

37 nks for e enion

6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas

6. Gas dynamics. Ideal gases Speed of infinitesimal disturbances in still gas 6. Gs dynmics Dr. Gergely Krisóf De. of Fluid echnics, BE Februry, 009. Seed of infiniesiml disurbnces in sill gs dv d, dv d, Coninuiy: ( dv)( ) dv omenum r r heorem: ( ( dv) ) d 3443 4 q m dv d dv llievi