NATL INST. OF STAND & TECH

AlllDS T7M3flS gg

I^EFEREIMCE Publications

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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KATIONAL BUREAU

OF STANDARDS UBHAPY 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

y-j = 170.368 + 0.605434 t - 1.33200 x 10"^ 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

Ay = -2.44358 x 10"^ + 1.17237 p + 0.125541 p^. (4)

Equations (3) and (4) were added together to synthesize the final

equation for calculating y:

-3 .2

y ca 1^ = y^ + Ay = 170.256 + 0.605434 t - 1.33200 x 10 " t

+ 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

.

meas .

,

in Table 1

.

The estimate of residual standard deviation (RSD), that is, the

estimate of the standard deviation of y^^i^ -y^^oc » ''s 0-^^ 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 y^^^^ , is 0.05^.

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

calc. y.--,_ = 17.0256 + 6.05434 x 10 " t -1.33200 x 10 " t

+ 0.117237 p + 1.25639 x 10'^ p^. (6)

For y in 10" 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

y^ = 167.225 + 0.392728 t + 1.22474 x 10"^ t^. (9)

The values of Ay were fitted by least squares to an equation quadratic

in p. The resulting equation is
Ay = -1.12860 X 10'^ + 1.24165 p + 9.87206 x 10'^ /. (10)

Equations (9) and (10) were added together to synthesize the final

equation for calculating y:

Vr..^. = 167.214 + 0.392728 t + 1.22474 x 10"^ 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... .. .n-4 .2 ^ II-* /xi/i -^ < \Jk y I y X V III M M It I I *. calc. y„-,. = 16.7214 + 3.92728 x 10 " t + 1.22474 x 10 " t

+ 0.124165 p + 9.87206 x

10""^ p^' (12)

For y in 10" lb ft" sec" , t in °C, and p in PSI_, equation (11) becomes

^ II • <.v\ < -*- y tr^ <VJI II 'M III -2 r, ^or.r.-7 JfllJ / »* Tn-5 I f 1 x2-f- calc. y.,n. = 11.2363 + 2.63901 x 10 ^ t + 8.22987 x 10 " t

+ 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

Ay = 0.133827 + 6.28105 x 10"^ p + 0.562974 p^. (16)

Equations (15) and (16) were added together to synthesize the final

equation for calculating y:

v^r.i. = 137.339 + 0.441133 t + 1.12987 x 10"^ t^ Cd I C

+ 6.28105 X 10"^ 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 . . . ,onn. -..-4 .2

calc. y_,-,_ = 13.7339 + 4.41133 x 10 " t + 1.12987 x 10 " t

+ 6.28105 X 10"^ p + 5.62974 x 10"^ p^. (18)

For y in 10" lb ft" sec" , t in °C, and p in PS I , equation (17) becomes

Uo.T. = 9.22876 + 2.96428 x 10"^ t + 7.59238 x 10"^ 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

Mt = Vr. = 185.946 + 0.530773 t - 1.04982 x 10"^ 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:

y T = 185.975 + 0.530773 t - 1.04982 x 10"^ t^

^calc.

6.99813 X 10"^

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.nn -,^-4 .2 ^ IX *-*\-l/»-» H- t-. <ll//< V III fi/iiii.# .. .*. calc. y„,-,_ = 18.5975 + 5.30773 x 10 " t - 1.04982 x 10 " t

- 6.99813 X 10"^

p. (23)

For y in 10" lb ft" sec" , t in °C, and p in PS I , equation (22) becomes

y^.i. = 12.4969 + 3.56663 x 10"^ t - 7.05446 x 10"^ 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
y-, = 208.940 -^ 0.702190 t - 3.30712 x 10"^ 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

Ay = 3.17420 X 10"^ + 1.73987 p + 0.152358 p^. (27)

Equations (26) and (27) were added together to synthesize the final

equation for calculating y:

y.=i. = 208.762 + 0.702190 t - 3.30712 x 10"^ \}

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

calc.

y__-,- = 20.8762 + 7.02190 x 10 ^ t - 3.30712 x 10 " t

+ 0.173987 p + 1.52358 x 10'^ p^. (29)

10
y , = 14.0282 + 4.71850 x 10"^ t - 2.22228 x 10"^ 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

y^ = 190.539 + 0.650043 t - 8.97542 x 10"^ 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:

^..1. = 190.395 + 0.650043 t - 8.97542 x 10'^ t^ calc.

+ 0.130897 p + 1.32418 x

10""^ 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

^calc " '•9.0395 + 6.50043 x 10"^ t - 8.97542 x 10"^ t^

+ 0.129185 p + 1.28975 x 10"^ p^. (35)

— fi -1 1 For y in 10" 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.

+ 5.98525 X 10"^

p + 4.11587 x 10"^ 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 Corresponding 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
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NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO,

NBS TT^ 1186

2. Performing Organ. Report No, 3. Publication Date February 1984

4. TITLE AND SUBTITLE

Interpolation Formulas for Viscosity of Six Gases:

Helium, Argon, and Oxygen

Air, Nitrogen, Carbon Dioxide:

5. AUTHOR(S)

Frank E. Jones

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

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;

0,4 £ p 5 40 atm) for the experimental data. The estimates of relative residual

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

\~X\ Unlimited

I I For Official Distribution. Do Not Release to NTIS

rX\ Order From Superintendent of Documents, U.S. Government Printing Office. Washington, D.C

20402. Q^ Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

26

15. Price

USCOMM-DC 6043-P80


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