NATL INST. OF STAND & TECH
AlllDS T7M3flS gg I^EFEREIMCE Publi- cations
I/) Q NBS TECHNICAL NOTE 1186 *
U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards
Interpolation Formulas for Viscosity of Six Gases: Air, Nitrogen, Carbon Dioxide, Helium, Argon, and Oxygen
103
. LI5753 Mo.llSC 1984 NATIONAL BUREAU OF STANDARDS
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Interpolation Formulas for ^^/
Viscosity of Six Gases: lOo ue)-?53 Air, Nitrogen, Carbon Dioxide, ^>o i^^ Helium, Argon, and Oxygen "i^f
Frank E. Jones
Center for Chemical Engineering National Engineering Laboratory National Bureau of Standards Washington, D C 20234
Q ft- \ ^^ftEAU O^
U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrlge, Secretary
NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
Issued February 1984 National Bureau of Standards Technical Note 1 1 86
Natl. Bur. Stand. (U.S.), Tech. Note 11 86, 26 pages (Feb. 1984) CODEN: NBTNAE
U.S. GOVERNMENT PRINTING OFRCE WASHINGTON: 1984
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, DC 20402 INTERPOLATION FORMULAS FOR VISCOSITY OF SIX GASES: AIR, NITROGEN, CARBON DIOXIDE, HELIUM, ARGON, AND OXYGEN
Frank E. Jones National Bureau of Standards Washington, DC 20234
Equations for the calculation of viscosity for dry air, nitrogen, carbon dioxide, helium, argon, and oxygen have been developed as interpolation formulas fitted to experimental data. The approximate ranges of strict application of the equations are the ranges of temperature (20°C £ t _< SO^C) and pressure (0.04 £ p £ 4 MPa; 0.4 <_ p < 40 atm) for the experimental data. The estimates of relative resTdual standard deviation for the fits (0.05% for air, 0.03% for nitrogen, 0.02% for carbon dioxide, 0.02% for helium, 0.03% for argon, and 0.03% for oxygen) are in close agreement with estimates of precision for the experimental data.
Key words: Air; argon; calculation; carbon dioxide; helium; nitrogen; oxygen; viscosity.
1. INTRODUCTION
In the calibration and use of flow metering devices the precise, accurate value of the viscosity of the gas being metered is often required. The availability of simple equations relating viscosity, y, to temperature, t, and pressure, p, would be a convenience to the engineer in calculating y. In the present work, simple interpolation formulas have been developed which enable the engineer to conveniently make precise, accurate calculations of y for dry air, nitrogen, carbon dioxide, helium, argon, and oxygen using small readily available hand-held calculators. The formulas are fitted to experimental data.
The data were selected from the literature on the basis of claimed accuracy and precision, and of internal consistency. The last of these criteria is particularly important for the development of empirical equations for volume flow with a dominant term of the Poiseuille form, the subject of a later paper. The sets of data published by Kestin and his collaborators [1-10] meet these criteria and have been used to develop the formulas.
2. EXPERIMENTAL DATA
The ranges of temperature and pressure of Interest in the present
work are 0°C <_ t _< 50°C and < p <_ 4 MPa (0 < p <_ 40 atm). The experimental data used in developing the equations for u are listed in
Tables 1-6. In Table 1 for dry air, the data in the first and third groups are taken from Table III of [1]; the second and fourth groups are taken from Table II of [2]; and the 50.00°C point is inferred from the data in [2], In Table 2 for nitrogen, the first and third groups are taken from Table XI of [1]; the second, fifth, and sixth groups are taken from Table VIII of [2]; the fourth group is taken from Table III of [3]; the 20.58°C point is taken from Table XI of [1]; and the
24.920°C point is taken from Table III of [3]. In Table 3 for carbon dioxide, the 20.00°C data are taken from Table V of [1]; the second group is taken from Table IV of [2]; and the 25.00°C point is taken from Table III of [4]. In Table 4 for helium, the first group is taken from Table VII of [1]; the 25.00°C point is taken from Table IV of [5]; and the third group is taken from Table V of [2]. In Table 5 for argon, the first and second groups are taken from Table IV of [1]; the third group is taken from Table IV of [3]; and the fourth group is taken from Table III of [2]. In Table 6 for oxygen, the first and second groups are adjusted values from Table XII of [1]; the third group is taken from Table V of [10]. 3. DEVELOPrCNT OF EQUATIONS
The equations for y (t,p) were developed using a procedure [6] in which u(t,p) is expressed as
y(t,p) = Pq (t,0) + Ay(p). (1)
where y (t,0) is the viscosity at "zero pressure" and Ay(p) is the
experimental value of viscosity, Vr^^p.^ > minus y (t,0). The procedure will be outlined below.
Air
The data pairs, (20.00°C, 181.94 yg/cm^s), (23.44°C, 183.75 yg/cm-s),
(23.90°C, 184.21 yg/cm-s), (25.00°C, 184.62 yg/cm-s), and (50.00°C, 197.31 yg/cm-s), taken from Table 1, were fitted by least squares to an equation quadratic in t to enable calculation of y at 0.101325 MPa, y-,. The small departures of p from this value of pressure for these pairs are not significant. The resulting equation is
= 10"^ y-j 170.368 + 0.605434 t - 1.33200 x t^, (2)
where y-, is in yg/cm-s and t is in °C. To reduce y-, to "zero pressure,"
y , the value of the increase in y per 0.10325 MPa, 0.11 yg/cm-s, estimated from the tabulated data was subtracted from y-. resulting in
y^ = 170.258 + 0.605434 t - 1.33200 x lO'"^ t^. (3)
Calculated values of y are listed in Table 1 . . . , . .
The difference, Ay, between the experimental values of y and calculated values of y is also listed in Table 1. The values of Ay were fitted by least squares to an equation quadratic in p. The resulting equation is
10"^ Ay = -2.44358 x + 1.17237 p + 0.125541 p^. (4)
Equations (3) and (4) were added together to synthesize the final equation for calculating y:
-3 .2 = + Ay = 170.256 + 0.605434 t - 1.33200 x 10 " t y ca 1^ y^
+ 1.17237 p + 0.125639 /, (5)
where y ,, is in ug/cin«s, t is in °C, and p is in MPa. Values of y^^i^ and caic. — Co I c differences between y^^^^ and experimental values, y^^^. , are listed ca I c me as . in Table 1
The estimate of residual standard deviation (RSD), that is, the
0-^^ estimate of the standard deviation of y^^i^ -y^^oc » ''s yg/cm-s for ca I c . me a 5 the 19 differences (n=19). The estimate of the relative residual standard
deviation (RRSD), that is, the ratio of RSD to the mean , is 0.05^. y^^^^me as
Kestin and Leidenfrost [1] estimated that for their measurements "a precision ranging from +0.01% to +^0.07%, depending on the gas, has been achieved. The final accuracy of the measurements is estimated to be of the order of +0.05%." DiPippo and Kestin [2] estimated the precision of their data to be +0.05%; they reached the conclusion that "no meaningful assessment of the accuracy of the present data can be given if by accuracy we mean the irreducible discrepancy between the best measurements available at any particular time." For y in yPa«s , t in ^, and p in MPa , equation (5) becomes
y.--,_ = 17.0256 + 6.05434 x 10 " t -1.33200 x 10 " t calc.
10'^ + 0.117237 p + 1.25639 x p^. (6)
10" For y in lb ft" sec" , t in ^, and p in PS I , equation (5) becomes
p = 11.4407 + 4.06833 x 10"^ t -8.95063 x 10"^ t^ ca I c.
+ 5.43165 X 10"^ p + 4.01338 x lO"'^ p^. (7)
Nitrogen
The data pairs, (20.58°C, 175.93 yg/cm-s), (21.98°C, 176.56 yg/cm-s),
(23.15°C, 177.05 yg/cm-s), (24.920°C, 177.94 yg/cm-s), (29.75°C, 180.08 yg/cm-s), and (49.37°C, 189.71 yg/cm-s), taken from Table 2, were fitted by least squares to an equation quadratic in t to enable calculation of y-,. The resulting equation is
y, = 167.335 + 0.392728 t + 1.22474 x 10"^ t^. (8)
To reduce y-, to y , 0.11 yg/cm-s estimated from the tabulated data was
subtracted from y, resulting in
10"^ y^ = 167.225 + 0.392728 t + 1.22474 x t^. (9)
The values of Ay were fitted by least squares to an equation quadratic
in p. The resulting equation is .
10'^ 10'^ Ay = -1.12860 X + 1.24165 p + 9.87206 x /. (10)
Equations (9) and (10) were added together to synthesize the final
equation for calculating y:
10"^ Vr..^. = 167.214 + 0.392728 t + 1.22474 x t^ ca I c
+ 1.24165 p + 9.87206 x 10'^ p^, (11)
where y-,-]- is in yg/cni'S , t is in ^, and p is in MPa,
The RSD is 0.05 yg/cm-s for n = 50; the RRSD is 0.03%. Kestin et. al.
[3] estimated the accuracy of their experimental measurements to be of the
order of +0.2% and the relative precision to be 0.03%. The accuracy and
precision estimates quoted above for air from [1] and [2] apply also to
nitrogen.
For y in yPa'S , t in ^, and p in MPa , equation (11) becomes
-2 . , . oo...M M It I I .. .n-4 .2*. y„-,. =^ 16.7214II-* /xi/i +-^ 3.92728< \Jk y I y X xV 10III " t + 1.22474 x 10 " t calc.
10""^ p^' + 0.124165 p + 9.87206 x (12)
10" For y in lb ft" sec" , t in °C, and p in PSI_, equation (11) becomes
-2 r, ^or.r.-7JfllJ / »* Tn-5I f 1 x2-f- y.,n. =^ 11.2363II • <.v\ < +-*- 2.63901y tr^ + 5.75263 X 10"^ p + 3.15351 x 10"^ p^. (13) . . Carbon Dioxide The data pairs, (20.00°C, 146.63 yg/cm-s), (25.00°C, 149.09 yg/cm-s), (30.40°C, 151.81 yg/cm-s), and (49.12°C, 161.75 yg/cm-s), taken from Table 3, were fitted by least squares to an equation quadratic in t to enable calculation of y-,. The resulting equation is y, = 137.335 + 0.441133 t + 1.12987 x 10"^ t^. (14) To reduce y-, to y , 0.13 yg/cm«s estimated from the tabulated data was subtracted from y-, resulting in u = 137.205 + 0.441133 t + 1.12987 x 10"^ t^. (15) The values of Ay were fitted by least squares to an equation quadratic in p. The resulting equation is 10"^ Ay = 0.133827 + 6.28105 x p + 0.562974 p^. (16) Equations (15) and (16) were added together to synthesize the final equation for calculating y: 10"^ v^r.i. = 137.339 + 0.441133 t + 1.12987 x t^ Cd I C 10"^ + 6.28105 X p + 0.562974 p^, (17) where y-^-i- is in yg/cm'S , t is in %^, and p is in MPa. The RSD is 0.04 yg/cm-sfor n = 11 ; the RRSD is 0.02%. Kestin et. al [4] estimated the accuracy of the 25.00°C point, "expressed as the maximum . estimated uncertainty in the quoted values," to be +0.1%. The accuracy and precision estimates quoted above for air from [1] and [2] apply also to carbon dioxide. For y in yPa'S , t in ^, and p in MPa_, equation (17) becomes -2 -..-4 . . . ,onn. .2 y_,-,_ = 13.7339 + 4.41133 x 10 " t + 1.12987 x 10 " t calc. + 6.28105 X 10"^ p + 5.62974 x 10"^ p^. (18) 10" For y in lb ft" sec" , t in °C, and p in PS I , equation (17) becomes 10"^ 10"^ Uo.T. = 9.22876 + 2.96428 x t + 7.59238 x t^ ca I c + 2.91005 X 10"^ p + 1.79836 x 10"^ p^. (19) Helium The data pairs, (20.00°C, 196.14 yg/cm-s), (24.28°C, 198.19 yg/cm-s), (25.00°C, 198.59 yg/cm-s), (30.56°C, 201.18 yg/cm-s), and (52.79°C, 211.04 yg/cm-s), were fitted by least squares to an equation quadratic in t to enable calculation of y-,. The effect of pressure on y for helium is so small that no correction is made to reduce y-, to y . The resulting equation is = = - 10"^ Mt Vr. 185.946 + 0.530773 t 1.04982 x t^. (20) The values of Ay were fitted by least squares to an equation linear in p. The resulting equation is Ay = 2.91664 X 10"^ - 6.99813 x 10"^ p. (21) Equations (20) and (21) were added together to synthesize the final equation for calculating y: = 185.975 + 0.530773 t - 1.04982 x 10"^ t^ y^calc.T 10"^ 6.99813 X p, (22) where y , is in yg/crri'S, t is in °C, and p is in MPa. calc. ^^^^ — The RSD is 0.04 yg/cm-s for n = 15; the RRSD is 0.02%. The accuracy and precision estimates quoted above for air from [1] and [2] apply also to helium. The 25.00°C °C value is estimated to be accurate within + 0.1% [5], For y in yPa^s , t in ^, and p in MPa , equation (22) becomes -2 . . r.nr.nnfi/iiii.# .. -,^-4 .2.*. y„,-,_ =^ 18.5975IX *-*\-l/»-» +H- 5.30773t-. - 6.99813 X 10"^ p. (23) 10" For y in lb ft" sec" , t in °C, and p in PS I , equation (22) becomes 10"^ 10"^ y^.i. = 12.4969 + 3.56663 x t - 7.05446 x t^ ca I c. 3.24228 X 10"^ p. (24) Argon The data pairs, (20.00°C, 222.86 yg/cm-s), (24.39°C, 225.79 yg/cm-s), (25.00°C, 226.36 yg/cm.s), and (50.31°C, 243.43 yg/cm-s), taken from Table 5 were fitted by least squares to an equation quadratic in t to enable calculation of y-. . The resulting equation is . -^ 10"^ y-, = 208.940 0.702190 t - 3.30712 x t^. (25) To reduce y-, to y , 0.21 yg/cm-s estimated from the tabulated data was subtracted from y-, resulting in ^ y^ = 208.730 + 0.702190 t - 3.30712 x 10 t^. (26) The values of Ay were fitted by least squares to an equation quadratic in p. The resulting equation is 10"^ Ay = 3.17420 X + 1.73987 p + 0.152358 p^. (27) Equations (26) and (27) were added together to synthesize the final equation for calculating y: 10"^ y.=i. = 208.762 + 0.702190 t - 3.30712 x \} ca 1 c + 1.73987 p + 0.152358 p^, (28) where u^^-i- is in yg/cm^s , t is in ^, and p is in MPa . The RSD is 0.07 yg/cm-s for n = 38; the RRSD is 0.03%. The estimates of accuracy and precision of the experimental data for argon are those quoted above from [1], [2], and [3]. For y in yPajs, t in °C, and p in MPa, equation (28) becomes -2 . . .n^no in-5 .2 y__-,- = 20.8762 + 7.02190 x 10 ^ t - 3.30712 x 10 " t calc. + 0.173987 p + 1.52358 x 10'^ p^. (29) 10 , 10"^ 10"^ y , = 14.0282 + 4.71850 x t - 2.22228 x t^ calc. + 8.06091 X 10"^ p + 4.86689 x lO"'' p^. (30) Oxygen The data pairs, (20.00°C, 203.17 ug/cm-s), (25.00°C, 206.25 yg/cm-s), (35.00°C, 212.18 yg/cm-s), and (50. 00^*0, 220.80 yg/cm-s) taken from Table 6, were fitted by least squares to an equation quadratic in t to enable calculation of yi- The resulting equation is 10"^ y^ = 190.539 + 0.650043 t - 8.97542 x t^. (31) To reduce y] to \Sq, 0.12 yg/cm-s estimated from the tabulated data was subtracted from y-] resulting in y^ = 190.419 + 0.650043 t - 8.97542 x 10"^ t^. (32) The values of Ay were fitted by least squares to an equation quadratic in p. The resulting equation is Ay = -0.0239595 + 0.130897 p + 1.323418 x 10"^ p^. (33) Equations (32) and (33) were added together to synthesize the final equation for calculating y: = 190.395 + 0.650043 t - 8.97542 x 10'^ t^ ^..1.calc. 10""^ + 0.130897 p + 1.32418 x p^ (34) 11 where locale. ^^ ^" Mg/cm-s , t is in ^, and p is in atm. The RSD is 0.06 g/cm s for n = 16; the RRSD is 0.03%. The estimates of accuracy and precision of the experimental data for oxygen are those quoted above from [1], [2], and [3]. For y in uPa-s , t in ^, and p in MPa , equation (34) becomes " '•9.0395 + 6.50043 x 10"^ t - 8.97542 x 10"^ ^calc t^ 10"^ + 0.129185 p + 1.28975 x p^. (35) — fi -1 1 10" For y in lb ft" sec" , t in **C, and p in PSI, equation (34) becomes ,^ = 12.7940 + 4.36809 x 10"^ t - 6.03121 x 10"^ t^ calc.^ 10"^ 10"^ + 5.98525 X p + 4.11587 x p^. (36) 4. RANGES OF APPLICATION OF THE EQUATIONS The equations developed in this paper are interpolation formulas fitted to experimental data. The range of strict application is indicated by the range of t and p of the experimental data listed in Tables 1-5. In the absence of measurements of y for temperatures below 20°C of comparable quality to that of the data in the tables, there are two options in extending calculations below 20" C (0 < t < 20*0): 1) apply the extended law of corresponding states [3,7-10]; 2) extrapolate using the equations developed here, with probable loss in accuracy. Either option might be followed until suitable experimental data at temperatures below 20''C became available. 12 . Hanley et al . [11] have developed a functional form to represent critically evaluated viscosity and thermal conductivity coefficient data, and have generated tables. The gases treated by Hanley et al include nitrogen and argon. Values of y calculated using the formulas in the present work have been compared with interpolated values from the tables in [11] at 0°C, S^C, 10"*C, IS^'C, 20''C, and 25°C, and 0.1 MPa, for nitrogen and argon. The deviation of the values in the present work from the values from reference [11], expressed in percent are: for nitrogen, +0.26% at O^C, +0.02% at S^C, -0.12% at 10°C, -0.28% at IS^'C, -0.32% at 20*0, and -0.38% at 25''C; for argon, -1.16% at 0°C, -1.10% at S^C, -0.99% at 10*^0, -0.86% at 15°C, -0.78% at 20''C, and -0.66% at 25°C. These deviations are all well within the uncertainty, j^ 2%, estimated by Hanley et al . for their tables. 5. CONCLUSIONS Equations (interpolation formulas fitted to experimental data) for the calculation of y for dry air, nitrogen, carbon dioxide, helium, argon, and oxygen have been developed. The estimates of relative residual standard deviation for the fits are in close agreement with the estimates of precision for the experimental data in the above stated ranges. 6. ACKNOWLEDGMENTS The author is deeply grateful to J. Kestin for his helpful suggestions and to him and his collaborators for the experimental data on which the present work is based. The typing of the manuscript by Susan Johnson is gratefully acknowledged. 13 . Nomenclature p = pressure RRSD = estimate of relative residual standard deviation RSD = estimate of residual standard deviation t = temperature in °C Ay = u -u meas. o y = viscosity = y ^i calculated value of viscosity ca I c = y_ experimental value of viscosity-^ meas. ^ y = viscosity at "zero pressure" y^ = viscosity at 0.101325 MPa 14 References 1. Kestin, J., and Leidenfrost, W., "An Absolute Determination of the Viscosity of Eleven Gases," Physica, Vol. 25, 1959, pp. 1033-1062. 2. DiPippo, R., and Kestin, J., "The Viscosity of Seven Gases up to 500°C and Its Statistical Interpretation," Proceedings Fourth Symposium on Thermophysical Properties , American Society of Mechanical Engineers, College Park, Md., 1958, pp. 304-313. 3. Kestin, J., Paykoc, E., and Sengers, J.V., "On the Density Expansion for Viscosity in Gases," Physica, Vol. 54, 1971, pp. 1-19. 4. Kestin, J., Ro, S.T. , and Wakeham, W.A., "Viscosity of Carbon Dioxide in the Temperature Range 25-700°C," J. Chem. Phys., Vol. 58, No. 8, 1972, pp. 4114-4118. 5. Kestin, J., Khalifa, H.E., Ro, S.T., and Wakeham, W. A., "The Viscosity and Diffusion Coefficients of Eighteen Binary Gaseous Systems," Physica, Vol. 88A, 1977, pp. 242-260. 6. Kestin, J., and Whitelaw, J.H., "The Viscosity of Dry and Humid Air," Int. J. Heat Mass Transfer, Vol. 7, 1964, pp. 1245-1255. 7. Kestin, J., Ro, S.T., and Wakeham, W.A., "An Extended Law of Corres- ponding States for the Equilibrium and Transport Properties of Noble Gases," Physica, Vol. 58, 1972, pp. 165-211. 8. Kestin, J., Ro, S.T., and Wakeham, W.A., "Viscosity of the Noble Gases in the Temperature Range 25-700°C," J. Chem. Phys., Vol. 56, No. 8, 1970, pp. 4119-4124. 9. Kestin, J., and Mason, E.A. , "Transport Properties in Gases (Comparison Between Theory and Experiment)," AIP Conf. Proc. No. 11, 1973, Edited by J. Kestin, pp. 137-192. 10. Hellemans, J.M., Kestin, J., and Ro, S.T., "The Viscosity of Oxygen and Some of Its Mixtures With Other Gases," Physica 65_, 1973, pp. 362-375, 11. Hanley, H.J.M., McCarty, R.D., and Haynes, W.M., "The Viscosity and Thermal Conductivity Coefficients for Dense Gaseous and Liquid Argon, Krypton, Xenon, Nitrogen, and Oxygen," J. Phys. Chem. Ref. Data 3^, 1974, pp. 979-1018. 15 ^ — w fO <— OJ CO E • i—t— I— O'^i— Ovj"^ o CM r— csj r~^ CO UD "^ ^ 3. b: OOOOOOOi— r— O r- I— o o O r— 1— O 1 O oooooooo o o o o o o o o o o o c_> cn + 11 I I I I + + I I I 1 + + + + + n— ;i fO '— o 3- LD r-. OO OJ '^ CTi (^ un r-. CM cri 03 CM CM CO CO "^ '=:3- CO -^ ';:r ^ r^ o C71 CO CO OD CO CO CO CO CO CO CO CO CO CO CO CO CO CTi cn CTl 7X w E '— LDi— cT^Lnr^Lnr^ COVJDr— ^r^OO IsOCMOJ CTiCO ;1CJ r-LnO>^0(~Dr— CO OOCOCMi— O 0"^iX) o-^ OO cm ooi— 1— cMCMcoLn o o o o o o o CM Ln o o ;3. 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CO cn r-^ CO CO I CO CO CO '::^ 00 CO E — ^ "^ cn cn cTi o cu CM CM ^ "^ '=^ cn 22 in (U in S* rO<*'d-fOl— OO r— 1— •SfCOCOOO co r— 3-e I— OOOOO O OOOi— o o o • • • I {^ •••••• ••••• "^ • ooQOoooo cpoooo ooo «— 3. o 3. ' trt r— O00'?^<«0L0l— r-> VO 00 «?1- IT) «;J- '>oy3y3i^<.o^o<^^o 1— r— i— r— 1— f— r~co 1— I— I— .— f— f— OU3 o o 00000000 u 3- cooorororororooo y3v£5U3i«o^o • • r~-i.OCT>ocMi— r^co T^ <7\ 10 00 OCMC0 00000000 OOOOO 000 Q.O 00000000 Lf) Lf) un LD LO Lf) LD O E — CMCMCMCMCMCMCMCM CM CM CM CM CM CM 00 UO 23 NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No, 3. Publication Date REPORT NO, BIBLIOGRAPHIC DATA TT^ 1186 February 1984 SHEET (See instructions) NBS 4. TITLE AND SUBTITLE Interpolation Formulas for Viscosity of Six Gases: Air, Nitrogen, Carbon Dioxide: Helium, Argon, and Oxygen 5. AUTHOR(S) Frank E. Jones 6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered WASHINGTON, D.C. 20234 Final 9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP) Same as item 6. 10. SUPPLEMENTARY NOTES [3J Document describes a computer program; SF-185, FlPS Software Summary, is attached. 11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here) Equations for the calculation of viscosity for dry air, nitrogen, carbon dioxide, helium, argon, and oxygen have been developed as interpolation formulas fitted to experimental data. The approximate ranges of strict application of the equations are tne ranges of temperature (20°C < t < 50°C) and pressure (0.04 < p < 4 MPa; of relative residual 0,4 £ p 5 40 atm) for the experimental data. The estimates standard deviation for the fits (0.05% for air, 0.03% for nitrogen, 0.02% for carbon dioxide, 0.02% for helium, 0.03% for argon, and 0.03% for oxygen) are in close agreement with estimates of precision for the experimental data. 12. KEY WORDS (S/x to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons) air; argon; calculation, carbon dioxide; helium; nitrogen; oxygen; viscosity 13. AVAILABILITY 14. NO. OF PRINTED PAGES \~X\ Unlimited 26 For Official Distribution. Do Not Release to NTIS I I rX\ Order From Superintendent of Documents, U.S. Government Printing Office. Washington, D.C 20402. 15. 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