Designation: D 2270 93 (Reapproved 1998)

Designation: 226/91 (95)

An American National Standard
British Standard 4459
Standard Practice for
Calculating Viscosity Index From Kinematic Viscosity at 40
and 100C
1
This standard is issued under the xed designation D 2270; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
This is also a standard of the Institute of Petroleum issued under the xed designation IP 226. The nal number indicates the year of
last revision.
This standard has been approved for use by agencies of the Department of Defense.
1. Scope
1.1 This practice
2
species the procedures for calculating
the viscosity index of petroleum products, such as lubricating
oils, and related materials from their kinematic viscosities at 40
and 100C.
3
1.1.1 Procedure AFor petroleum products of viscosity
index up to and including 100.
1.1.2 Procedure BFor petroleum products of which the
viscosity index is 100 or greater.
1.2 Table 1 given in this practice applies to petroleum
products with kinematic viscosities between 2 and 70 mm
2
/s
(cSt) at 100C.
4
Equations are provided for calculating viscos-
ity index for petroleum products having kinematic viscosities
above 70 mm
2
/s (cSt) at 100C.
1.3 The kinematic viscosity values are determined with
reference to a value of 1.0038 mm
2
/s (cSt) at 20.00C for
distilled water. The determination of the kinematic viscosity of
a petroleum product shall be carried out in accordance with
Test Methods D 445, IP 71, ISO 3104, or ISO 2909.
1.4 The values stated in SI units are to be regarded as the
standard.
2. Referenced Documents
2.1 ASTM Standards:
D 341 Viscosity-Temperature Charts for Liquid Petroleum
Products
5
D 445 Test Method for Kinematic Viscosity of Transparent
and Opaque Liquids (and the Calculation of Dynamic
Viscosity)
5
D 1695 Terminology of Cellulose and Cellulose Deriva-
tives
6
2.2 ISO Standards:
ISO 2909 Petroleum productsCalculation of Viscosity
Index from kinematic viscosity
7
ISO 3104 Petroleum productsTransparent and opaque
liquidsDetermination of kinematic viscosity and calcu-
lation of dynamic viscosity
7
2.3 IP Document:
IP 71
8
3. Terminology
3.1 Denitions of Terms Specic to This Standard:
3.1.1 viscosity index, nan arbitrary number used to char-
acterize the variation of the kinematic viscosity of a petroleum
product with temperature.
3.1.1.1 DiscussionFor oils of similar kinematic viscosity,
the higher the viscosity index the smaller the effect of tem-
perature on its kinematic viscosity.
NOTE 1Viscosity index is also used in Terminology D 1695 in a
denition unrelated to that in 3.1.1.
1
This practice is under the jurisdiction of ASTM Committee D-2 on Petroleum
Products and Lubricants and is the direct responsibility of Subcommittee D02.07 on
Flow Properties.
In the IP, this practice is under the jurisdiction of the Standardization Committee.
Current edition approved March 15, 1993. Published May 1993. Originally
published as D 2270 64. Last previous edition D 2270 91.
2
Metrication of Viscosity Index System Method D 2270 is available fromASTM
Headquarters. Request RR: D02-1009.
3
The results obtained from the calculation of VI from kinematic viscosities
determined at 40 and 100C are virtually the same as those obtained from the former
VI system using kinematic viscosities determined at 37.78 and 98.89C.
4
1 cSt = 1 mm
2
/s = 10
6
m
2
/s.
5
Annual Book of ASTM Standards, Vol 05.01.
6
Annual Book of ASTM Standards, Vol 06.03.
7
Available fromAmerican National Standards Institute, 11 W. 42nd St., 13th Fl.,
New York, NY 10036.
8
Available from Institute of Petroleum, 61 New Cavendish St., London W1M
8AR, United Kingdom.
1
Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
TABLE 1 Basic Values for L and H for Kinematic Viscosity in 40100C System
Kinematic
Viscosity
at
100C,
mm
2
/s
(cSt)
L H
Kinematic
Viscosity
at 100C,
mm
2
/s
(cSt)
L H
Kinematic
Viscosity
at 100C,
mm
2
/s
(cSt)
L H
Kinematic
Viscosity
at 100C,
mm
2
/s
(cSt)
L H
Kinematic
Viscosity
at 100C,
mm
2
/s
(cSt)
L H
Kinematic
Viscosity
at 100C,
mm
2
/s
(cSt)
L H
2.00 7.994 6.394 7.00 78.00 48.57 12.0 201.9 108.0 17.0 369.4 180.2 24.0 683.9 301.8 42.5 1935 714.9
2.10 8.640 6.894 7.10 80.25 49.61 12.1 204.8 109.4 17.1 373.3 181.7 24.2 694.5 305.6 43.0 1978 728.2
2.20 9.309 7.410 7.20 82.39 50.69 12.2 207.8 110.7 17.2 377.1 183.3 24.4 704.2 309.4 43.5 2021 741.3
2.30 10.00 7.944 7.30 84.53 51.78 12.3 210.7 112.0 17.3 381.0 184.9 24.6 714.9 313.0 44.0 2064 754.4
2.40 10.71 8.496 7.40 86.66 52.88 12.4 213.6 113.3 17.4 384.9 186.5 24.8 725.7 317.0 44.5 2108 767.6
2.50 11.45 9.063 7.50 88.85 53.98 12.5 216.6 114.7 17.5 388.9 188.1 25.0 736.5 320.9 45.0 2152 780.9
2.60 12.21 9.647 7.60 91.04 55.09 12.6 219.6 116.0 17.6 392.7 189.7 25.2 747.2 324.9 45.5 2197 794.5
2.70 13.00 10.25 7.70 93.20 56.20 12.7 222.6 117.4 17.7 396.7 191.3 25.4 758.2 328.8 46.0 2243 808.2
2.80 13.80 10.87 7.80 95.43 57.31 12.8 225.7 118.7 17.8 400.7 192.9 25.6 769.3 332.7 46.5 2288 821.9
2.90 14.63 11.50 7.90 97.72 58.45 12.9 228.8 120.1 17.9 404.6 194.6 25.8 779.7 336.7 47.0 2333 835.5
3.00 15.49 12.15 8.00 100.0 59.60 13.0 231.9 121.5 18.0 408.6 196.2 26.0 790.4 340.5 47.5 2380 849.2
3.10 16.36 12.82 8.10 102.3 60.74 13.1 235.0 122.9 18.1 412.6 197.8 26.2 801.6 344.4 48.0 2426 863.0
3.20 17.26 13.51 8.20 104.6 61.89 13.2 238.1 124.2 18.2 416.7 199.4 26.4 812.8 348.4 48.5 2473 876.9
3.30 18.18 14.21 8.30 106.9 63.05 13.3 241.2 125.6 18.3 420.7 201.0 26.6 824.1 352.3 49.0 2521 890.9
3.40 19.12 14.93 8.40 109.2 64.18 13.4 244.3 127.0 18.4 424.9 202.6 26.8 835.5 356.4 49.5 2570 905.3
3.50 20.09 15.66 8.50 111.5 65.32 13.5 247.4 128.4 18.5 429.0 204.3 27.0 847.0 360.5 50.0 2618 919.6
3.60 21.08 16.42 8.60 113.9 66.48 13.6 250.6 129.8 18.6 433.2 205.9 27.2 857.5 364.6 50.5 2667 933.6
3.70 22.09 17.19 8.70 116.2 67.64 13.7 253.8 131.2 18.7 437.3 207.6 27.4 869.0 368.3 51.0 2717 948.2
3.80 23.13 17.97 8.80 118.5 68.79 13.8 257.0 132.6 18.8 441.5 209.3 27.6 880.6 372.3 51.5 2767 962.9
3.90 24.19 18.77 8.90 120.9 69.94 13.9 260.1 134.0 18.9 445.7 211.0 27.8 892.3 376.4 52.0 2817 977.5
4.00 25.32 19.56 9.00 123.3 71.10 14.0 263.3 135.4 19.0 449.9 212.7 28.0 904.1 380.6 52.5 2867 992.1
4.10 26.50 20.37 9.10 125.7 72.27 14.1 266.6 136.8 19.1 454.2 214.4 28.2 915.8 384.6 53.0 2918 1007
4.20 27.75 21.21 9.20 128.0 73.42 14.2 269.8 138.2 19.2 458.4 216.1 28.4 927.6 388.8 53.5 2969 1021
4.30 29.07 22.05 9.30 130.4 74.57 14.3 273.0 139.6 19.3 462.7 217.7 28.6 938.6 393.0 54.0 3020 1036
4.40 30.48 22.92 9.40 132.8 75.73 14.4 276.3 141.0 19.4 467.0 219.4 28.8 951.2 396.6 54.5 3073 1051
4.50 31.96 23.81 9.50 135.3 76.91 14.5 279.6 142.4 19.5 471.3 221.1 29.0 963.4 401.1 55.0 3126 1066
4.60 33.52 24.71 9.60 137.7 78.08 14.6 283.0 143.9 19.6 475.7 222.8 29.2 975.4 405.3 55.5 3180 1082
4.70 35.13 25.63 9.70 140.1 79.27 14.7 286.4 145.3 19.7 479.7 224.5 29.4 987.1 409.5 56.0 3233 1097
4.80 36.79 26.57 9.80 142.7 80.46 14.8 289.7 146.8 19.8 483.9 226.2 29.6 998.9 413.5 56.5 3286 1112
4.90 38.50 27.53 9.90 145.2 81.67 14.9 293.0 148.2 19.9 488.6 227.7 29.8 1011 417.6 57.0 3340 1127
5.00 40.23 28.49 10.0 147.7 82.87 15.0 296.5 149.7 20.0 493.2 229.5 30.0 1023 421.7 57.5 3396 1143
5.10 41.99 29.46 10.1 150.3 84.08 15.1 300.0 151.2 20.2 501.5 233.0 30.5 1055 432.4 58.0 3452 1159
5.20 43.76 30.43 10.2 152.9 85.30 15.2 303.4 152.6 20.4 510.8 236.4 31.0 1086 443.2 58.5 3507 1175
5.30 45.53 31.40 10.3 155.4 86.51 15.3 306.9 154.1 20.6 519.9 240.1 31.5 1119 454.0 59.0 3563 1190
5.40 47.31 32.37 10.4 158.0 87.72 15.4 310.3 155.6 20.8 528.8 243.5 32.0 1151 464.9 59.5 3619 1206
5.50 49.09 33.34 10.5 160.6 88.95 15.5 313.9 157.0 21.0 538.4 247.1 32.5 1184 475.9 60.0 3676 1222
5.60 50.87 34.32 10.6 163.2 90.19 15.6 317.5 158.6 21.2 547.5 250.7 33.0 1217 487.0 60.5 3734 1238
5.70 52.64 35.29 10.7 165.8 91.40 15.7 321.1 160.1 21.4 556.7 254.2 33.5 1251 498.1 61.0 3792 1254
5.80 54.42 36.26 10.8 168.5 92.65 15.8 324.6 161.6 21.6 566.4 257.8 34.0 1286 509.6 61.5 3850 1270
5.90 56.20 37.23 10.9 171.2 93.92 15.9 328.3 163.1 21.8 575.6 261.5 34.5 1321 521.1 62.0 3908 1286
6.00 57.97 38.19 11.0 173.9 95.19 16.0 331.9 164.6 22.0 585.2 264.9 35.0 1356 532.5 62.5 3966 1303
6.10 59.74 39.17 11.1 176.6 96.45 16.1 335.5 166.1 22.2 595.0 268.6 35.5 1391 544.0 63.0 4026 1319
6.20 61.52 40.15 11.2 179.4 97.71 16.2 339.2 167.7 22.4 604.3 272.3 36.0 1427 555.6 63.5 4087 1336
6.30 63.32 41.13 11.3 182.1 98.97 16.3 342.9 169.2 22.6 614.2 275.8 36.5 1464 567.1 64.0 4147 1352
6.40 65.18 42.14 11.4 184.9 100.2 16.4 346.6 170.7 22.8 624.1 279.6 37.0 1501 579.3 64.5 4207 1369
6.50 67.12 43.18 11.5 187.6 101.5 16.5 350.3 172.3 23.0 633.6 283.3 37.5 1538 591.3 65.0 4268 1386
6.60 69.16 44.24 11.6 190.4 102.8 16.6 354.1 173.8 23.2 643.4 286.8 38.0 1575 603.1 65.5 4329 1402
6.70 71.29 45.33 11.7 193.3 104.1 16.7 358.0 175.4 23.4 653.8 290.5 38.5 1613 615.0 66.0 4392 1419
6.80 73.48 46.44 11.8 196.2 105.4 16.8 361.7 177.0 23.6 663.3 294.4 39.0 1651 627.1 66.5 4455 1436
6.90 75.72 47.51 11.9 199.0 106.7 16.9 365.6 178.6 23.8 673.7 297.9 39.5 1691 639.2 67.0 4517 1454
40.0
40.5
41.0
41.5
42.0
1730
1770
1810
1851
1892
651.8
664.2
676.6
689.1
701.9
67.5
68.0
68.5
69.0
69.5
4580
4645
4709
4773
4839
1471
1488
1506
1523
1541
70.0 4905 1558
D 2270
2
4. Signicance and Use
4.1 The viscosity index is a widely used and accepted
measure of the variation in kinematic viscosity due to changes
in the temperature of a petroleum product between 40 and
100C.
4.2 A higher viscosity index indicates a smaller decrease in
kinematic viscosity with increasing temperature of the lubri-
cant.
4.3 The viscosity index is used in practice as a single
number indicating temperature dependence of kinematic vis-
cosity.
5. Procedure AFor Oils of Viscosity Index Up to and
Including 100
5.1 Calculation:
5.1.1 If the kinematic viscosity of the oils at 100C is less
than or equal to 70 mm
2
/s (cSt), extract from Table 1 the
corresponding values for L and H. Measured values that are not
listed, but are within the range of Table 1, may be obtained by
linear interpolation. The viscosity index is not dened and may
not be reported for oils of kinematic viscosity of less than 2.0
mm
2
/s (cSt) at 100C.
5.1.2 If the kinematic viscosity is above 70 mm
2
/s (cSt) at
100C, calculate the values of L and H as follows:
L 5 0.8353 Y
2
1 14.67 Y 2 216 (1)
H 5 0.1684 Y
2
1 11.85 Y 2 97 (2)
where:
L = kinematic viscosity at 40C of an oil of 0 viscosity
index having the same kinematic viscosity at 100C as
the oil whose viscosity index is to be calculated,
mm
2
/s (cSt),
Y = kinematic viscosity at 100C of the oil whose viscos-
ity index is to be calculated, mm
2
/s (cSt), and
H = kinematic viscosity at 40C of an oil of 100 viscosity
index having the same kinematic viscosity at 100C as
the oil whose viscosity index is to be calculated mm
2
/s
(cSt).
5.1.3 Calculate the viscosity index, VI, of the oil as follows:
VI 5 @~L 2 U!/~L 2 H!# 3 100 (3)
where:
U = kinematic viscosity at 40C of the oil whose viscosity
index is to be calculated mm
2
/s (cSt).
5.1.4 Calculation Example:
Measured kinematic viscosity at 40C of the oil whose
viscosity index is to be calculated = 73.30 mm
2
/s (cSt)
kinematic viscosity at 100C of the oil whose viscosity index
is to be calculated = 8.86 mm
2
/s (cSt)
From Table 1 (by interpolation) L = 119.94
From Table 1 (by interpolation) H = 69.48
Substituting in Eq 3 and rounding to the nearest whole
number:
VI 5 @~119.94 2 73.30!/~119.94 2 69.48!# 3 100 5 92.43 (4)
VI 5 92 (5)
5.2 ASTM DS 39b
9
Viscosity Index Tables for Celsius Tem-
peratures is based on the above calculation and may be used
instead of 5.1-5.1.4.
6. Procedure BFor Oils of Viscosity Index of 100 and
Greater
6.1 Calculation:
6.1.1 If the kinematic viscosity of the oil at 100C is less
than or equal to 70 mm
2
/s (cSt), extract the corresponding
value for H from Table 1. Measured values that are not listed,
but are within the range of Table 1, can be obtained by linear
interpolation. The viscosity index is not dened and may not be
reported for oils of kinematic viscosity of less than 2.0 mm
2
/s
(cSt) at 100C.
6.1.2 If the measured kinematic viscosity at 100C is greater
than 70 mm
2
/s (cSt), calculate the value of H as follows:
H 5 0.1684 Y
2
1 11.85 Y 2 97 (6)
where:
Y = kinematic viscosity at 100C of the oil whose kine-
matic viscosity is to be calculated, mm
2
/s (cSt), and
H = kinematic viscosity at 40C of an oil of 100 viscosity
index having the same kinematic viscosity at 100C as
the oil whose viscosity index is to be calculated mm
2
/s
(cSt).
6.1.3 Calculate the viscosity index, VI, of the oil as follows:
VI 5 @~~antilog N! 2 1!/0.00715# 1 100 (7)
where:
N 5 ~ log H 2 log U!/ log Y, (8)
or
Y
N
5 H/U (9)
where:
U = kinematic viscosity at 40C of the oil whose viscosity
index is to be calculated mm
2
/s (cSt).
6.1.4 Calculation Example:
(1) Measured kinematic viscosity at 40C of the oil whose
viscosity index is to be calculated = 22.83 mm
2
/s (cSt)
kinematic viscosity at 100C of the oil whose viscosity index
is to be calculated = 5.05 mm
2
/s (cSt)
From Table 1 (by interpolation) H = 28.97
Substituting by Eq 8 (by logarithms):
N 5 @~log 28.97 2 log 22.83!/log 5.05# 5 0.14708 (10)
Substituting in Eq 7 and rounding to the nearest whole number:
VI 5 @~~antilog 0.14708! 2 1!/0.00715# 1 100 (11)
5 @~1.40307 2 1!/0.00715# 1 100 5 156.37
VI 5 156
(2) Measured kinematic viscosity at 40C of the oil whose
viscosity index is to be calculated = 53.47 mm
2
/s (cSt) kine-
matic viscosity at 100C of the oil whose viscosity index is to
be calculated = 7.80 mm
2
/s (cSt)
From Table 1, H = 57.31
Substituting in Eq 8 (by logarithms):
9
Available from ASTM Headquarters.
D 2270
3
N 5 @~ log 57.31 2 log 53.47!/log 7.80# 5 0.03376 (12)
Substituting in Eq 7 and rounding to the nearest whole number:
VI 5 @~~antilog 0.03376! 2 1!/0.00715# 1 100 (13)
5 @~1.08084 2 1!/0.00715# 1 100 5 111
6.2 ASTM DS 39b
6
Viscosity Index Tables for Celsius
Temperatures is based on the above calculation and may be
used instead of 6.1 through 6.1.4.
7. Report
7.1 Report the viscosity index to the nearest whole number.
When the number is exactly halfway between the nearest two
whole numbers, round to the nearest even number.
7.2 Calculated viscosity index numbers can differ depend-
ing on the kinematic viscosity data as determined. When
duplicate kinematic viscosity data are available, it is recom-
mended that viscosity index values calculated therefrom be
considered acceptable only when the kinematic viscosity data
meet the acceptability limits in Test Method D 445 of 0.35 %
for repeatability and 0.70 % for reproducibility. It is also
recommended that the viscosity index calculated and reported
be that based on the means of the appropriate kinematic
viscosity values. If the kinematic viscosity data do not meet
acceptability limits in Test Method D 445, the data should be
examined and redetermined.
8. Precision and Bias
8.1 The calculation of viscosity index from kinematic vis-
cosities at 40 and 100C is exact, and no precision limits can be
assigned to this calculation.
8.2 The accuracy of the calculated viscosity index is depen-
dent only on the accuracy of the original viscosity determina-
tion. Test Method D 445 has a stated repeatability limit of
0.35 % and a reproducibility limit of 0.70 %.
8.3 See Appendix X1 for a discussion of the precision that
can be attributed to the viscosity index.
8.4 BiasThe calculation of viscosity index from kine-
matic viscosities at 40 and 100C is exact, and no bias can be
assigned to this calculation.
9. Keywords
9.1 kinematic viscosity; viscosity index
APPENDIXES
(Nonmandatory Information)
X1. VISCOSITY INDEX CALCULATIONS FROM KINEMATIC VISCOSITIES AT NON-STANDARD
TEMPERATURES
X1.1 In certain cases, it is of interest to obtain the VI of an
oil when conditions prevent the use of the standard tempera-
tures of 40 and 100C. An estimate may be made by calculating
the kinematic viscosity at 40C and 100C from data obtained
at other temperatures. Reference should be made to Viscosity-
Temperature Charts D 341 for the suitable equations. The
kinematic viscosity data used should preferably be taken from
temperatures near the standard values and as widely separated
as possible.
X1.2 Viscosity index values of an oil calculated from
non-standard data as discussed above should be considered as
suitable for information only and not desirable for specication
purposes.
X1.3 Precision Attributed to Viscosity Index:
X1.3.1 It is sometimes important to know the precision that
can be attributed to the viscosity index values, especially so as
to not place undue importance on small differences between a
calculated value of the viscosity index on the same material
determined within a laboratory on different days, and also
those determined between laboratories.
X1.3.2 Viscosity index repeatability and reproducibility
were given in the precision section of this test method. These
calculations
10,11
are based on the assumption that the overall
kinematic viscosity determinations would be within the preci-
sion of Test Method D 445.
X1.3.3 The data on which Fig. X1.1 is based are calculated
on the worst case assumption in the precision section of this
test method, and show a greater variation in the viscosity index
than had been shown in the D2270 77 precision section.
Thus, for example, two laboratories can report on the same
sample of oil the following data:
Laboratory
No. 1 No. 2
Kinematic viscosity at 100C (mm
2
/s) 12.95 13.04
Kinematic viscosity at 40C (mm
2
/s) 145.0 144.0
Viscosity index (unrounded) 77.91 80.25
Viscosity index (rounded) 78 80
These data are within the precision of Test Method D 445,
and demonstrate at 13 cSt at 100C the maximum difference in
the VI.
X1.3.4 For Fig. X1.1 the repeatability of viscosity index is
one-half of the value for the reproducibility of viscosity index.
X1.3.5 If the calculated viscosity indexes are rounded to
whole numbers before comparison, this may cause their
difference to exceed the precision limits to be attributed to the
10
Marmin, A. J., and Sommelet, Peter, Viscosity Index Repeatability and
Reproducibility, Journal of Materials, ASTM, June 1972, p. 206.
11
Bayle, G. G., Latitudes of Viscosity Index Values, Journal of Testing and
Evaluation, ASTM, Vol 5, No. 3, May 1977, pp. 154160.
D 2270
4
viscosity index without the experimental kinematic viscosities
being mutually inconsistent. In case of doubt, therefore, it is
advisable to compare viscosity index data before rounding (that
is, to include the rst decimal place when making the
comparison).
X2. OTHER COMPUTATIONAL METHODS
X2.1 The exact computational method for the calculation of
viscosity index is dened in Sections 5 and 6 of this test
method. However, computation by computer or programmable
calculator may be desired. This appendix describes three
methods.
X2.2 The calculation of viscosity index requires:
X2.2.1 Input of kinematic viscosity data at 40 and 100C.
X2.2.2 Calculation of L and H corresponding to the kine-
matic viscosity at 100C.
X2.2.3 Calculation of the viscosity index using equations in
Sections 5 and 6 of this test method.
X2.3 Values of L and H can be determined as follows:
X2.3.1 The complete table of L and H can be stored in
computer memory. Values of L and H calculated using linear
interpolation will be exactly the same as those calculated in this
test method. This table requires a relatively large section of
computer memory, but ensures exact calculation of L, H, and
viscosity index.
X2.3.2 Alimited few entries in Table 1 may be stored in the
computer memory. To calculate L corresponding to the given
value Y of kinematic viscosity at 100C, select the data pair
from Table X2.1 that is nearest the given kinematic viscosity
value. Select also the data pair above and below this data pair.
Using these three data pairs, calculate the coefficients a, b, and
c in the equation:
L 5 a Y
2
1 b Y 1 c (X2.1)
In a similar manner calculate the coefficients to the equation:
H 5 d Y
2
1 e Y 1 f (X2.2)
The 32 sets of data in Table X2.1 have been selected from
Table 1, and represent a balance between the minimum number
of sets of data items and acceptable accuracy of the quadratic
FIG. X1.1 Reproducibility of Viscosity Index
TABLE X2.1 Data Pairs for Quadratic Interpolation of L and H
Kinematic Viscosity
at 100C, mm
2
/s
(cSt)
L H
Kinematic Viscosity
at 100C, mm
2
/s
(cSt)
L H
2.0 7.994 6.394 12 201.9 108.0
2.9 14.63 11.50 13.5 247.4 128.4
3.8 23.13 17.97 15 296.5 149.7
4.1 26.50 20.37 16.5 350.3 172.3
4.4 30.48 22.92 18 408.6 196.2
4.7 35.13 25.63 20 493.2 229.5
5.0 40.23 28.49 24 683.9 301.8
5.7 52.64 35.29 28 904.1 380.6
6.4 65.18 42.14 34 1286 509.6
6.7 71.29 45.33 40 1730 651.8
7.0 78.00 48.57 47.5 2380 849.2
7.4 86.66 52.88 55 3126 1066
7.8 95.43 57.31 62.5 3966 1303
8.4 109.2 64.18 70 4905 1558
9.0 123.3 71.10 100 9604 2772
10.5 160.6 88.95 130 15810 4290
D 2270
5
interpolation calculations for L and H. Other choices for Table
X2.1 can be made to t the computer memory available and the
required accuracy of the calculation of L and H.
X2.3.3 The data in Table 1 can also be t to a series of
quadratic equations. The range of each equation must be
consistent with acceptable accuracy for all values of L and H
within its range. One set of sixteen equations is given in Table
X2.2; the errors in individual values of L and H so calculated
are believed not to exceed 0.1 %. For a given value of Y, select
the pair of equations whose range includes this value of Y and
calculate directly the values of L and H.
X2.4 With the given values of Y and U and the calculated
values of L and H corresponding to Y from X2.2, the viscosity
index is calculated directly using
X2.4.1 (Eq 3) where U $ H or
X2.4.2 (Eq 7) and (Eq 8) where U # H as is described in
Section 6 of this test method.
X2.5 An example of these methods is as follows:
given kinematic viscosity at 40C = 73.50 mm
2
/s (cSt)
and kinematic viscosity at 100C = 8.86 mm
2
/s (cSt).
X2.5.1 Using the method described in X2.3.1 to calculate L
and H, the look-up table stored in computer memory.
Kinematic Viscosity,
mm
2
/s at 100C L H
8.8
8.9
118.5
120.9
68.79
69.94
linear interpolation gives
L 5 119.94 (X2.3)
H 5 69.48
X2.5.2 Using Table X2.1 as described in X2.3.2, the three
sets of data selected from computer memory are
Kinematic Viscosity
at 100C L H
8.4 109.2 64.18
9.0 123.3 71.10
10.5 160.6 88.95
from which are calculated
L 5 0.65079 Y
2
1 12.1762 Y 2 39.00 (X2.4)
H 5 0.17460 Y
2
1 8.4952 Y 2 19.50 (X2.5)
for the range of Y between 8.4 and 9.0. For Y = 8.86
L 5 119.9681 (X2.6)
H 5 69.4741 (X2.7)
X2.5.3 As described in X2.3.3, the equations stored in
memory which include Y = 8.86 are
L 5 0.41858 Y
2
1 16.1558 Y 2 56.040 (X2.8)
H 5 0.05794 Y
2
1 10.5156 Y 2 28.240 (X2.9)
(a) From the given value of Y = 8.86 mm
2
/s (cSt)
L 5 119.9588 (X2.10)
H 5 69.4765 (X2.11)
X2.5.4 Since U $ H
Viscosity index 5 @~L 2 U!/~L 2 H!# 3 100 (X2.12)
(a) For the data in X2.5.1
VI 5
119.94 2 73.50
119.94 2 69.48
3 100 5 92.033 5 92 (X2.13)
(b) For the data in X2.5.2
VI 5
119.9681 2 73.50
119.9681 2 69.4741
3 100 5 92.027 5 92 (X2.14)
(c) For the data in X2.5.3
VI 5
119.9588 2 73.50
119.9588 2 69.4765
3 100 5 92.030 5 92 (X2.15)
TABLE X2.2 Coefficients of Quadratic Equations (Eq 1 and Eq 2)
Y
min
Y
max
a b c d e f
2.0 3.8 1.14673 1.7576 0.109 0.84155 1.5521 0.077
3.8 4.4 3.38095 15.4952 33.196 0.78571 1.7929 0.183
4.4 5.0 2.5000 7.2143 13.812 0.82143 1.5679 0.119
5.0 6.4 0.10100 16.6350 45.469 0.04985 9.1613 18.557
6.4 7.0 3.35714 23.5643 78.466 0.22619 7.7369 16.656
7.0 7.7 0.01191 21.4750 72.870 0.79762 0.7321 14.610
7.7 9.0 0.41858 16.1558 56.040 0.05794 10.5156 28.240
9.0 12 0.88779 7.5527 16.600 0.26665 6.7015 10.810
12 15 0.76720 10.7972 38.180 0.20073 8.4658 22.490
15 18 0.97305 5.3135 2.200 0.28889 5.9741 4.930
18 22 0.97256 5.2500 0.980 0.24504 7.4160 16.730
22 28 0.91413 7.4759 21.820 0.20323 9.1267 34.230
28 40 0.87031 9.7157 50.770 0.18411 10.1015 46.750
40 55 0.84703 12.6752 133.310 0.17029 11.4866 80.620
55 70 0.85921 11.1009 83.19 0.17130 11.3680 76.940
70 Up 0.83531 14.6731 216.246 0.16841 11.8493 96.947
L = a Y
2
+ b Y + c
H = d Y
2
+ e Y + f
D 2270
6
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D 2270
7