ASTM D2162 Test Method for Basic Calibration of Master Viscometers and Viscosity Oil Standards
10. Corrections and Calculation of Kinematic Viscosity at 40°C
10.1 Buoyancy Correction (Applicable to Both Cannon and Ubbelohde Viscometers):
10.1.1 In kinematic viscometers the driving head of liquid is slightly reduced by the counterpoised head of air in the empty arm of the viscometer. This buoyancy effect is measured by the density of air divided by the density of the liquid. In going from water at 20°C to oil at another temperature, the net effect is the difference between the two as follows:
cb = (da20 / dw20) - (daT / doT)
where:
cb = buoyancy correction expressed as a fraction of the driving head.
da20 = density of moist air at 20°C (0.00120 g/mL),
dw20 = density of water at 20°C (0.998 g/mL),
daT = density of moist air at the test temperature, g/mL (see Table 1), and
doT = density of oil at the test temperature, g/mL.

10.1.2 Determine the density of the oil standard at 40°C in accordance with Test Method D1480. Alternatively, determine the relative density of the oil at some convenient temperature and obtain the relative density at 40°C in accordance with Guide D1250. Relative density is close enough to density for the purposes of this correction.

10.1.3 Calculate the buoyancy correction by the equation given in 10.1.1, inserting the determined oil density at 40°C and the density of air at 40°C from Table 1. For most petroleum oils the approximate buoyancy correction is -0.0002 when correcting from water at 20°C to oil at 40°C.

10.2 Temperature Correction (Necessary only with Cannon-type viscometer and only when test temperature differs from the calibration temperature, 20°C):
10.2.1 The effects of thermal expansion of glass capillary-tube viscometers of the kinematic type are virtually self-compensating and usually may be neglected. However, in viscometers in which the working volume is fixed at 20 +/- 3°C but which are used at another temperature, the driving head changes with expansion or contraction of the liquid. The correction is given as follows:
cT = V(dT - d20) / pR2hdT
where:
cT = temperature correction expressed as a fraction of the driving head,
V = total volume of fill at 20°C, mL,
d20 = density of the liquid when filled at 20°C, g/mL,
dT = density of the liquid at the test temperature, g/mL,
R = inside radius of the reservoir, cm, and
h = driving head, cm, at 20°C.

NOTE 7 - The volume of fill, the inside radius of the reservoir, and the driving head may be measured approximately since errors in these measurements have only slight effects on the final corrected viscosity. For Cannon masters conforming to the dimensions shown in Fig. 1 the equation reduces to:
cT = 0.023 x [(dT - d20) / dT]

10.2.2 Determine the density of the oil at 20°C in accordance with Test Method D1480. Alternatively, determine the relative density of the oil at some convenient temperature and obtain the relative density at 20°C and 40°F in accordance with Guide D1250. Relative density may be substituted for density in this equation.

10.2.3 Calculate the temperature correction by the equation given in 10.2.1, inserting the density of the oil at 20°C and the density of the oil at 40°C as determined in 10.1 or as calculated in accordance with Guide D1250. For most petroleum oils the approximate temperature correction is -0.0003 when correcting from 20°C to 40°C.

10.3 Surface Tension Correction (Necessary only with the Cannon-type viscometer, when calibrated with one liquid and used with another liquid having a different surface tension and density):
10.3.1 If the upper liquid meniscus in a viscometer flows in a narrower tube than the bottom meniscus, the driving head is slightly reduced by the capillary rise in the smaller diameter tube or bulb. The surface tension and capillary rise of water are greater than that of oil. Consequently, the driving head is reduced more with water in the viscometer and the driving head is less with water in the viscometer than it is with oil. A correction is required for the difference in capillary rise of water and oil.

10.3.2 Equations have been derived relating capillary rise to surface tension in tubes of small diameter. These equations are not exact when applied to larger tubes. The corrections given in Table 2 are based upon actual measurements of capillary rise with both water and oil in a bulb simulating the Cannon master efflux bulb. They are empirical corrections to be applied only to Cannon master viscometers having the dimensions shown in Fig. 1. The efflux bulb must be spherical and have a volume of 3.0 cm3, the lower reservoir must have a diameter of 30 mm, and the head must be 470 +/- 40 mm.

10.3.3 Determine the surface tension of the oil standard at 40°C in accordance with Test Methods D1590.

10.3.4 Divide surface tension by density at 40°C as determined in 10.1.2. Select the surface tension correction from Table 2. The correction is expressed as a fraction of the driving head.

NOTE 8 - In Cannon master viscometers, the approximate surface tension correction for most petroleum oils is +0.0014 when correcting from water at 20°C to oil at 40°C. In Ubbelohde master viscometers the surface tension correction will be nearly zero if the diameter of the meniscus in the vent bulb below the capillary is 75 % that of the meniscus in the efflux bulb at the maximum diameter. If the diameter of the lower meniscus varies from 70 to 80 % of the maximum upper meniscus diameter, the surface tension correction, cs, will vary from -0.0002 to +0.0002 (-0.02 to +0.02 %); when the viscometer is made as shown in Fig. 2, the surface tension correction should be within these limits. If the diameter of the lower meniscus varies from 60 to 90 % of the maximum upper meniscus diameter, the surface tension correction, cs, will vary from -0.0005 to +0.0005 (-0.05 to +0.05 %).

10.4 Kinematic Viscosity Calculation:
10.4.1 For a Cannon master viscometer, calculate the kinematic viscosity of the oil standard as follows:
v = (1 + cb + cT + cs) x Ct
where:
v = kinematic viscosity of the oil at 40°C, mm2/s2 (cSt/s),
cb = buoyancy correction (see 10.1),
cT = temperature correction (see 10.2),
cs = surface tension correction (see 10.3),
C = calibration constant of master viscometer with water at 20°C, mm2/s 2 (cSt/s), and
t = average efflux time, s.

10.4.2 For a Ubbelohde master viscometer, calculate the kinematic viscosity of the oil standard as follows:
v = (1 + cb) x Ct
where:
v, c b, C, and t are as given in 10.4.1.

NOTE 9 - The value of (1 + cb + cT + cs) will average about 1.0009 for the Cannon master and 0.9998 for the Ubbelohde master viscometer. The total correction is therefore of the same order or below the repeatability limit of this test method.

10.5 Repeat the calculation for the data obtained in 9.7 with the second master viscometer. Average the kinematic viscosities if they agree within 0.1 %.