Library, N.w. Bldg /

FEB 4 1963

NBS MONOGRAPH 55

NBS Viscometer Calibrating Liquids

And Capillary Tube Viscometers

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANOAROS
THE NATIONAL BUREAU OF STANDARDS

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the back cover.

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available from the Superintendent of Documents, Government Printing Office, Washington 25, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

NBS Viscometer Calibrating Liquids

and Capillary Tube Viscometers

R. C. Hardy

National Bureau of Standards Monograph 55

Issued December 26, 1962

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. Price 20 cents
Contents

Page

1. Introduction 1

2. Viscometer calibrating liquids 3

3. NBS viscometer calibrating liquids 4

3.1. Newtonian character 4

3.2. Temperature coefficient of viscosity 5

3.3. Precision 5

3.4. Stability 6

4. API and ASTM oil standards 7

5. Relative capillary tube viscometers 7

6. Calibration of relative capillary tube viscometers 9

6.1. Variation in value of g 10

6.2. Curvature of the capillary 11

6.3. Heating effect 11

6.4. Drainage error and use of external pressure 11

6.5. Alinement 12

6.6. Effect of thermal expansion of the instrument 12

6.7. Correction for temperature of filling 13

6.8. Correction for temperature of run 14

6.9. Air column correction . 15

6.10. Correction for surface tension effects 15

7. Calibration of viscometers with reference viscometer 19

8. Precalibrated viscometers 20

9. References 20

10. Symbols 21
NBS Viscometer Calibrating Liquids and Capillary Tube Viscometers

R. C. Hardy

Most measurements of viscosity are made with relative viscometers. These instruments must be calibrated with liquids whose viscosities are known. NBS provides a

series of 10 oils for this purpose. Their viscosities range from 0.02 to 450 poises and

their temperature coefficients of viscosity range from 2.1 to 9.4 percent per degree C. When properly stored the oils may remain usable for from two months to one year but

prompt use is recommended. The less viscous oils are more stable. Representative

types of glass capillary tube viscometers and their use are discussed briefly. Contrary

to common belief, it is not necessary to calibi'ate these instruments at the temperature

of use since the temperature cofficients of the instruments are small and correction if necessary can be calculated. Instruments in which the effective volume of charge is not

adjusted at the test temperature may require adjustment of their calibration constants

to compensate for thermal expansion of the test liquid. Correction formulas for this

and other errors or conditions are presented.

1. Introduction

For many years the National Bureau of

Standards has supplied oil samples of known

viscosity to other laboratories for use in calibrating their viscometers. The need for a

publication describing this service and its purpose has been evident from time to time. This

paper is intended to fulfill that need and to

supply general information on the calibration

of capillary tube viscometers. Although some

of the errors and corrections discussed are

small and may be inconsequential even in rather

precise work, it seems worthwhile to mention

them so that if they are disregarded it can be

on the basis that due consideration warrants it rather than on the basis of oversight. Also, it is to be expected that continuing advances in

technology will require improved precision in

viscosity measurements for commercial purposes and more precise information on the viscosity of materials may permit refinements in

our concepts of molecular relations in the

liquid state.

The following discussion is limited to consideration of Newtonian or simple liquids and

to determinations of their viscosities. A Newtonian or simple liquid is a true liquid, i.e., a substance which will flow under the influence

of any finite shearing stress, for which the rate

of shear at any point is proportional to the

shearing stress at that point, and for which

the ratio of shearing stress to rate of shear

(commonly referred to as the viscosity of the

liquid) is determined solely by its composition,

temperature, and pressure. Although we may

speak of a material as being Newtonian or nonNewtonian as though this were a fixed characteristic, it should be remembered that its

behavior may change with changes in its temperature and pressure. To illustrate, one need

only point to the freezing of water or the gradual liquefaction or solidification of butter. The

eflfects of pressure are not readily apparent to

the senses but may be demonstrated in the

laboratory.

All measurements of viscosity are based on

Newton's hypothesis relative to laminar flow of

liquids. Broadly stated, this hypothesis is that

at any point in a liquid undergoing laminar

flow, the shearing stress causing flow is proportional to the rate of shear at that point. The

constant of proportionality in this relation is

known as the coeflScient of viscosity or merely

as the viscosity of the liquid.

The generally accepted equation for laminar

flow through cylindrical tubes of circular sec- tion is

where Q is. the volume rate of flow, r the radius

of the tube, ?? the viscosity of the liquid, and P'

is the pressure drop through a portion of the

tube of length I' in which the flow is not modified by the nearness of the ends.

This relation was derived from Newton's

hypothesis relative to laminar flow after Poiseuille had established the empirical relation

P D*

Q = K ——, (2)

t where D is the diameter of the tube, P the

pressure drop through the tube of length I, and

K a constant for a given liquid at a given temperature. This equation was based on the

results of an extensive series of very careful

1
observations of the rate of flow of water

through fine glass capillaries at various temperatures and pressures. In most of this work

the tubes were long in relation to their diameters so that the effects of the ends were negligible and differences between P and P' and between I and I' were negligible. Under these

conditions, the equivalence of the two equations is evident if we note that

16r* = and set K - —-—

.

12877

However, some of Poiseuille's observations

were made with relatively short tubes or with

high rates of flow and the results did not support eq (2) as well as would be expected in

view of the precision of the work. It should be

noted that eq (2) considers only the viscous

resistance of the liquid and ignores the fact

that some of the pressure drop between the

ends of the tube represents conversion of potential energy to the kinetic energy of the

stream issuing from the capillary. Hagenbach

was the first to point this out in a published

paper and to propose a correction for it. Subsequently, Couette proposed a correction

to account for the viscous resistance in the supply reservoir and the increased viscous resistance in the entrance portion of the tube where

the central portions of the stream are being

accelerated with respect to the peripheral portions as the velocity distribution in the stream

is changing from the more or less uniform distribution at the entrance to the theoretical

parabolic distribution in portions of the tube

remote from the entrance. Couette proposed

that this correction be made as a hypothetical

increase, X, in the length of the tube. The

magnitude of this correction is usually con- sidered to be proportional to the radius of the

tube, i.e., A = nr, where n is known as the coefficient of the Couette correction.

The change in potential energy of a volume,

V, of liquid as it flows from the entrance

reservoir to the exit reservoir is PV. Part of

this is converted to thermal energy in overcoming viscous resistance to flow in the tube and

supply reservoir, and the remainedr is con- verted to the kinetic energy of the stream issuing from the tube. Then we may write the following energy equation:

py^Ml±J^V + ^Y, (3)

77 T* 77^ r*

p where — V is the kinetic energy of the

77^ liquid passing any cr-oss section of the capillary

where the distribution of velocities is parabolic,

in time t. Solving eq (3) for r], we get

77Pr* t m pV

rj = ^- (4)

SVil + nr) S^{1 + nr)t

where an empirical factor m has been inserted

in an attempt to account for unknown conditions of flow near the ends.

This factor m is known as the coefficient of

the kinetic energy or Hagenbach correction.

Equation (1) is commonly referred to as Poiseuille's equation and eq (4) as the corrected

Poiseuille equation.

Dorsey [1]^ maintains that it is incorrect to

refer to the term containing m as the Hagenbach or kinetic energy correction and suggests

that the term is much more properly described

as an inertia correction. However, by a somewhat different line of reasoning he arrives at

the same relation expressed in eq (4). From

published data he concluded that for the ideal

case- n = 1.146 and m = 0 when the flow is

characterized by a Reynolds number ^Rg =

of 10 or less. But where Re > 10, n = 0.573

and m = 1. Dorsey recognized that in a real

instrument slight departures from ideal conditions may require modification of these values

and that there is not an abrupt change at

R„ = 10.

Various values for n and m based on theory

or experiment have been proposed. Most of

these fall in the range zero to a little more than

unity, although some experimental values several times as great have been reported. It is

usually assumed that n is a constant for a given

viscometer and a similar assumption is often

made for m although there is experimental

evidence that such is not true and that the

value of m is variable and a function of Re. It may be noted that for a parabolic distribution

of velocities the value of m would be unity and

for uniform velocity, 0.5. Uniform velocity across the stream would, of course, require

slippage at the wall to account for all relative

motion between the tube and the liquid. Transition from more or less uniform velocity at the

entrance to the theoretical parabolic distribution some distance within the tube is easily

visualized and would account for values of m

between 0.5 and 1. Experimental values outside this range might find explanation in an

inadequate correction for the Couette effect or

distortion of the parabolic distribution due to

temperature gradients resulting from the con- version of potential to thermal energy, or to

deviations from the theoretic shape of the tube

as a right circular cylinder.

Heating in the peripheral portion of the

stream is greater than in the central portion

because the velocity gradients are greater in

this region. This would tend to reduce the viscosity in the peripheral region and permit the

' Figures in brackets indicate literature references on page 20.

' The ideal case considered by Dorsey is the flow of a liquid from

a large reservoir, through a cylindrical capillary of circular cross

section, into a second large reservoir, the free liquid surface in each

reservoir being great in comparison with the sectional area of the

capillary, which is sharp-edged with large terminal faces normal to

its axis.

2
central portion to "slip through" in somewhat

plug fashion, leading to abnormally high kinetic

energy in the stream and requiring use of a

value for m somewhat greater than unity.

The assumption that the velocities are uniform, or virtually so, at the entrance to the tube

simplifies theoretical estimation of the entrance

effect and may be reasonably appropriate for

tubes with widely flared (trumpet shaped)

mouths fed from large reservoirs. However,

this leads to considerable uncertainty in the

values for I and r of the tube. It appears that

appropriate values for n and m for any given

instrument might be influenced somewhat by

the sizes and shapes of the terminal reservoirs

as well as the shapes of the ends of the tube.

Because of the uncertainty as to the proper

values for n and m, it is necessary either to

make careful estimates based on experimental

evidence of appropriate values for each instrument or to choose an instrument and test

conditions such that the corrections will not

have significant magnitude.

Using the relations expressed in eq (4) it is

possible to design and construct a capillary

tube viscometer and to measure the viscosity of

a liquid without reference to any standard for

viscosity. In such a case, the instrument would

be classed as an absolute viscometer and the

method would be referred to as an absolute

method.

It is very difficult to make accurate absolute

measurements of viscosity because of the difficulties of selecting a suitable capillary tube,

measuring its dimensions with suitable accuracy, and then determining suitable values for

n and m. On the other hand, it is relatively

easy to make accurate comparisons of the viscosities of two liquids. Instruments used for

making such comparisons are called relative

viscometers but they may be used to determine

absolute viscosities as well as relative, specific, or kinematic viscosities. To avoid confusion it may be well to point out that absolute viscosity^

means merely viscosity, the modifier "absolute"

being used only for emphasis and to point out

that reference is not being made to one of the

ratios involving viscosity, which for brevity are

often referred to as "viscosity." Relative or

specific viscosity is the ratio of the viscosity of a liquid at some temperature and pressure to

the viscosity of the same or another liquid at

the same or different temperature and pressure. Kinematic viscosity is the ratio of the

viscosity of a liquid to its density at the same

temperature and pressure. Absolute viscosities,

i.e., true viscosities, are measured in terms of

units having the dimensions mt^t-^ or FtH,

e.g., 1 poise = 1 gram per centimeter-second

or 1 reyn = 1 pound (wt) -second per square

inch, etc. Relative or specific viscosities are dimensionless numbers. Kinematic viscosity

is stated in terms of units having the dimensions I'-t^, e.g., in the cgs system, 1 stoke =

1 square centimeter per second.

2. Viscometer Calibrating Liquids

Most viscosity measurements are made with

relative viscometers, the use of which rests on

the availability of suitable reference standards

for viscosity. To be suitable for such use a liquid should be Newtonian, have the desired

viscosity, and be reasonably stable with regard

to aging.

A Newtonian liquid is one for which, at a given temperature and pressure, the ratio of

shearing stress to rate of shear is constant,

i.e., independent of the .rate of shear. It is

very important that a reference liquid be Newtonian since, in general, for any given liquid,

temperature, and pressure, not only will the

rate of shear be different in different instruments but in most instruments the rate of

shear will be different at different points in the

liquid, and in kinematic viscometers the rate

of shear at any given point will vary somewhat

during a measurement.

The viscosity of freshly distilled water at

20 °C has been determined accurately by an

absolute method [2] and found to be 0.010019±

0.000003 poise, the second number indicating

the estimated accuracy of the first. The proposal

to use the rounded off value 0.01002 poise has

been generally accepted and freshly distilled

water at 20 °C is widely used as the primary

reference standard for calibrating relative viscometers. Since many viscometers are not suitable for use with liquids as fluid as water, it is

necessary to calibrate them with other liquids

whose viscosities have been determined by direct comparison with water at 20 °C or by indirect comparison through one or more intermediate liquids and instruments.

Properly selected petroleum oils have been

found suitable for use as intermediate or secondary reference standards if they are considered to be only temporary standards. They

are multicomponent solutions of unknown composition and the viscosity of each lot or batch

must be determined. If for any reason—age or

possible contamination—the applicability of

this determined value is questioned, confidence

can be restored only by redetermining the viscosity of the sample, since there is no process

of repurification which can be relied upon to

restore the sample to its original composition

and viscosity.

•"• Use of the phrase "dynamic viscosity" to denote absolute vis- cosity is deprecated as unnecessary and undesirable in view of (a) the longstanding usage of the adjective "absolute" in this and

other fields to signify pure or fundamental and (b) the established usage of the phrase dynamic viscosity in connection with the flow

resistance of materials which exhibit frequency-dependent response

to a shearing force whose direction is reversed periodically.

3
The use of pure chemical compounds as ref- erence standards for viscosity has been suggested, the underlying thought being that once

the viscosity of the pure compound had been

determined, the material could be prepared independently in other laboratories, or that if a sample of the material became suspect because

of age or possible contamination, full confidence

in the sample could be restored by a suitable

routine purification process. However, at present, pure liquid chemical compounds suitable

for the purpose are not available in sufficient

quantities and techniques for preparing them

or for checking their purity are too specialized

for most laboratories. Some use has been made

of aqueous solutions of sucrose [3] and other

substances, but for various reasons these solutions do not provide suitable reference stand3. NBS Viscometer

Somewhat over 30 years ago the Bureau un- dertook a program to assist other laboratories

in the measurement of viscosities by obtaining

a series of capillary tube viscometers, calibrating them with reference to water, and using

these instruments to measure the viscosities of a series of oils, samples of which were sold to

other laboratories for use in calibrating viscometers. Originally six or seven oils were provided. The current series of oils, which was

started in 1938, consists of 10 hydrocarbon oils

with viscosities ranging from about 0.02 to 450

poises. A descriptive list of these oils is given

in table 1. The spacing of members of this

series was arranged to provide a substantially

continuous spectrum of viscosity values over

this range by varying the temperature of each

oil over the range 20 to 40 °C. Viscosity values

at other temperatures in the range 20 to 100 °C

(30 to 100 °C for Oil P) are determined and re- ported as a special service for which an additional charge is made. Strict adherence to the

plan for spacing of the oils would require Oils

Table 1. NBS viscometer calibrating oils^

Oil

Absolute viscosity, in poises, at Kinematic viscosity, in stokes, at

20 °C 25 °C 100 °F 210 °F 20 "C 25 °C 100 °F 210 °F

D

H

IJK

L

M

N

OB

0.020

.074

.12

.21

.41 1.0

3.0 14

0.018

.063

.10

.17 .32

.74 2.1 9.6

0.014

.044

.066

.11 .18

.37

1.0 4.0

0.006

.013

.017 .023

.032

.049

.099

.25

0.026

.091

.14

.25 .48

1.1 3.4 16

0.023

.078

.12

.21 .38

.84

2.4 11

0.019

.055

.081

.13 .22

.43

1.1 4.6

0.008

.017 .022

.028

.040

.060

.12

.30

20 °C 25 °C 30 °C 40 "C 50 °C 20 °C 25 °C 30 °C 40 °C 50 °C

300 200 55 200 350 210 60 450 95 510 220 100

" Oils SB and SF are not listed because they are intended only

for use with Saybolt Universal and Saybolt Furol viscometers, re- spectively. These instruments are not considered in this discussion.

ards for general use, chiefly perhaps because of

the difficulty of determining the concentrations

of the solutions with sufficient accuracy and of j maintaining the desired concentration sufficiently constant. Silicone fluids are somewhat ^ less sensitive to temperature changes than

^ petroleum oils, but this advantage is generally

overbalanced by the difficulty of cleaning the

viscometers after use of the silicone fluids.

Since the primary reference standard, freshly distilled water, can be prepared readily in

any well-equipped laboratory and used as a

basis for calibrating viscometers and a series j of secondary reference standards covering a j wide range of viscosity, it seems obvious that i the Bureaiu has no unique advantage in this

field over other well-equipped laboratories. !

I Calibrating Oils

A, B, and C with viscosities intermediate to Oil

D and water at 20 °C and Oils E, F, and G with

viscosities intermediate to Oils D and H. No

real need for these six oils has appeared and

they have not been prepared. Due to the relaj tively high sensitivity of the more viscous oils 1 to temperature, their spacing seemed rather i wide and Oil OB was added between Oil 0

(designation changed to Oil OA) and Oil P. The , material used for Oil 0 (OA) subsequently ' proved unsuitable and it was discontinued.

As the original lots of these oils became ex- hausted, they were replaced with similar oils

of approximately the same viscosity and as- ; signed the same letter designation with a j numercial suffix indicating the number of re-

| placement lots, e.g., D, D-1, D-2, etc. Later, to

| minimize some misunderstanding that these ^ were actually different oil standards, the designations were changed to indicate the situation

more clearly, e.g., Oil D, lot 10; Oil D, lot 11, ; etc.Oils D through L of the series are prepared

from stocks of three commercial "white" oils.

Oils M and N originally were high quality, nonj additive, commercial motor oils of SAE 30 and

70^ grades, respectively. With changing conditions, these oils became unsuitable for use as l viscometer calibrating liquids. Currently Oil N

is a Pennsylvania bright stock and Oil M is a blend of this and the most viscous of our white

oil stocks. Oils OB and P are polyisobutenes.

3.1. Newtonian Character

As stated above, it is important that viscometer calibrating liquids be Newtonian. This

statement appears simple enough until we try

to apply it practically. Since some materials

may deviate only slightly from Newtonian behavior, our classification will depend upon the

• The SAE classification has been revised and grades 60 and 70, discontinued.
sensitivity of our method for detecting nonNewtonian behavior. This reduces to the precision of viscosity determinations at different

rates of shear and the range of shear rates

which can be covered.

For the low rates of shear attainable with

the glass capillary tube viscometers used for

determining the viscosities of the NBS viscometer calibrating oils, there appears no basis

for questioning their Newtonian character.

Tests of the more viscous oils with instruments

of somewhat less precision but usable over a wide range of shear rates have indicated Newtonian behavior could be expected at shear

rates up to 1,000 sec \

In this connection it should be pointed out

that all viscosity measurements involve the

transformation of mechanical to thermal en- ergy with the development of temperature, and

hence viscosity, gradients in the liquid.

This inherent heating error is difficult to as- sess because of the interdependence of the

various factors involved, such as rate of shear

and design of the instrument, the thermal

capacity and conductance of the liquid, as well

as its temperature coefficient of viscosity, and

the thermal properties of the instrument and

its surroundings.

Although proper design and operation can

reduce the effects of heating due to shear, more

uncertainty must attach to measurements made

at the higher shear rates. When high accuracy

is required, calibrations and measurements

should be made at shear rates low enough that

the heating effect will be negligible.

Oils OB and P are polybutenes. In view of

the ample evidence in the literature that many

polymers are non-Newtonian, it may be pointed

out that although this behavior may be quite

pronounced and typical in very high molecular

weight polymers, it apparently is not typical of

low molecular weight polymers. Porter and

Johnson [4] report that polybutenes with

molecular Weights below some critical value of

about 17,000 are Newtonian. The molecular

weights of Oils OB and P have been estimated

to be about 1,500 to 2,100, respectively. Some

qualitative tests for the development of stress

in a direction normal to that of shear have indicated that Oils OB and P are not strictly

Newtonian, although the deviations from Newtonian behavior apparently are too slight to be

demonstrated by variation of their viscosities

with rate of shear.

3.2. Temperature Coefficient of Viscosity

Approximate values for the temperature coefficient of viscosity of these oils at various

temperatures are given in table 2. Table 3

presents this information in a reciprocal form,

i.e., the changes in temperature which would

cause a change of 0.1 percent in viscosity. The

higher temperature sensitivity of the more visTable 2. Percentage change in per 1 °C

T • -A JLjIQUIQ

Temperature

20 °C 25 °C 100 °F 100 °C

Water 2.44 2.27 1.94 1.04 Oil D 2.11 1.99 1.74 1.08 H 3.42 3.20 2.69 1.43

I 4.02 3.68 3.10 l!54 J 4.61 4.19 3.53 1.71 K 5.45 5.09 4.15 1.96 L b.ocs 5.84 4.87 2.28 M 7.27 6.80 5.72 2.62 N 8.03 7.39 6.32 3.13 OB 9.41 9.05 7.6 ^.12 P (8.72 at (7.03 at 4.52 30 °C) 50 "O

Table 3. Approximate temperature change causing

change of 0.1 % in ri

Liquid

Temperature

20 "G 25 °C 100 °F 100 °C

Water 0.041 0.044 0.058 0.096

Oil D .047 .050 .057 .092 H .029 .031 .037 .070

I .025 .027 .032 .065 J .022 .024 .028 .058 K .018 .020 .025 .051 L .016 .017 .020 .044 M .014 .015 .017 .038 N .012 .013 .016 .032 OB .011 .011 .013 .024 P (0.11 at (.014 at .022 30 °C) 50 °C)

cous oils often raises the question as to the

possibility of replacing these oils with liquids

having lower temperature sensitivity. While

some improvement in this may be possible, it does not appear likely that this difference in

sensitivity between the low and high viscosity

oils can be eliminated, since all experimental

data appear to indicate a general rule that

liquids having high viscosity have high temperature coefficients of viscosity and that for

any given liquid the temperature coefficient of

viscosity is high at temperatures where the

viscosity is high. It appears inevitable that

when working with high viscosity liquids we

must use closer temperature control to obtain

viscosity measurements with an accuracy comparable to that obtained with lower viscosity

liquids or be satisfied with lower precision and

accuracy.

3.3. Precision

Until about 1954 all viscosity values for the

NBS oils were determined with one of a series

of Bingham variable pressure viscometers.

After completion of a careful study of the calibration of the Bingham viscometers and of the

Cannon Master viscometers [5] it was decided

to use the latter type instruments for determining viscosity values lower than about 30 poises,

which appeared to be the upper limit of the

useful range of our series of Cannon Master

viscometers. We have continued to use the

Bingham instruments for determining higher

5
viscosity values. The Cannon Master viscometers yield measurements of the ratio of viscosity to density or kinematic viscosity. The

densities of the oils at several temperatures in

the range 20 to 100 °C are determined with a

dilatometer and values at other temperatures

determined by interpolation or extrapolation.

Values for absolute viscosity are obtained by

multiplying the value for kinematic viscosity

by the density at the appropriate temperature.

A statistical analysis of data obtained in the

most recent recalibration of our Cannon Master

viscometers indicated that the coefficient of

variance in the water calibrations was 0.015

percent for the average of three observations

by one of three operators chosen at random.

For the calibration of the whole series of instruments, only one operator was used and in

some instances several fillings of an instrument

were made with the same oil and sometimes

more than three observations of the flow time

for a filling were made. The coefficient of variance for the instrument constants varied from

0.002 percent for the water-calibrated instrument to 0.032 percent for the instruments with

the highest range. The coefficient of variance

for the viscosity values of the calibrating oils

ranged from 0.016 percent for Oil D to 0.031

percent for Oil N and another oil with kinematic viscosity of 25 stokes. A similar statistical study has not been made with the Bingham viscometers, but in the work reported in

reference [5] viscosity values obtained with the

two types of instruments agreed within 0.05

percent.

3.4. Stability

The viscometer calibrating oils supplied by

the Bureau are not permanent standards; hence

changes in their physical and chemical properties may be expected with age. Results of a

recent statistical analysis of available data on

the stability of these oils are summarized in

table 4. The raw data consisted of the viscosity

values determined at three temperatures for

various lots of each oil at known (but irregular) time intervals. Complete sets of data were

not available for all lots.

The indicated or apparent changes of viscosity with age and the precision were determined for each lot at each temperature. These

values were expressed as a percentage of the

viscosity in order that values at the different

temperatures could be averaged to obtain single

values for rate of change and precision for each

oil. The results were~ consistent with the as- sumption that for any given oil the percentage

change in viscosity and the precision would be

independent of temperature.

Columns 2 and 3 of table 4 show a tally of

the indicated decreases and increases of viscosity with age. For Oils D through L, the preTable 4. Change of viscosity with age"

Oil

D. HI.J. K.

L. M.

NOB

P.

Decreases

1816

1122

1823

2

2

2

Increases

12

1423

1020

331630

35

35

Rate

%/Mo

--0.0051 -- .0137 -- .0251 -- .0137

Precision'"

%

0.021

.033

.029 .022

.017 .033

.065

.041 .072

.055

Uncertainty

after issue"=

Mo

1212

12

12

12

12

66

2

6

0.10

.10 .10

.10

.10

.10

.25

.25 .30 .30

" For Oils M, N, OB, and P deviations for each temperature were

taken from the line 7;=a+6t where t is age when measurement was made.

s

*> Mean of average for each of three temperatures of 100 — for

n each lot. Based on indicated mean rate of change with age and including an allowance of three times the standard deviation for random

errors of measurement.

ponderance of changes in one direction over the

number of changes in the other direction is not

statistically significant at the 5 percent level.

That is to say, the data do not constitute con- vincing evidence that the viscosities of these

oils change with age. The 1:2 and 2:1 ratios

for Oils I and J may appear significant when

not considered statistically; but the possible

significance disappears if we consider further

that Oils I, J, and K are mixtures of the same

two base oils in different proportions and note

the lack of correlation between ratios and composition. The combined tally for the three oils

is 51 and 53.

For Oils M, N, OB, and P there is an obvious

and statistically significant preponderance of

positive rates over negative rates and it is

clear that the viscosities of these oils do in- crease with age. The rates of increase shown

in column 4 are based on the slopes of the least

squares lines representing change of viscosity

with age. A least squares line was computed

for each lot of oil at three temperatures insofar

as data were available. The precision of the

measurements (i.e., 100 times the estimated

standard deviation, S, divided by the viscosity,

77) are shown in column 5. For Oils M, N, OB,

and P, the estimates of precision are based on

deviations from the least squares lines. Columns

6 and 7 show the uncertainties which attach to

the reported viscosity values at stated ages

after shipment. These estimates include an

allowance of three times the standard deviation

for random errors of measurement. It is as- sumed that the samples have not been opened

and have been stored in the dark at normal

room temperature. It should be noted that

while the data did not present convincing

evidence that Oils D through L change with age,

they are too few and cover insufficient time intervals to warrant the assumption that these

oils will not change if aged sufficiently. Further,

the estimates in column 7 are based on the com6
posite picture presented by at least several lots

of each oil and any given lot may be expected

to deviate somewhat from the average. Consequently it is recommended that the oils be used

as soon as convenient after they are received.

In no event should oils which have been on

hand for periods significantly greater than

those listed be considered as standards with

accuracies comparable to those of reasonably

current standards.

4. API and ASTM Oil Standards

The viscometer calibrating liquids supplied

by the Bureau are not absolute standards and

similar series of calibrating liquids or working

standards may be prepared independently in

other laboratories. A number of the petroleum

companies have facilities for this. The American petroleum industry through the American

Petroleum Institute has for many years supplied a few oil standards for calibrating or checking the calibration of viscometers. These

standards were intended primarily for use in

petroleum laboratories and originally were calibrated only in terms of the Saybolt viscosity

scales. Later, in cooperation with the American

Society for Testing Materials, the viscosities of

these API oils were reported in terms of kinematic viscosity. Recently this series has been

expanded to provide a range almost as wide as the NBS series and the sponsorship transferred

to ASTM. These oils are now being supplied by

a commercial laboratory under contract with

ASTM and under the supervision of an ASTM

5. Relative Capillary

No attempt will be made to consider all the

various forms of capillary tube viscometers

which are or have been used for relative measurements.

A few types are shown in figure 1 and a brief

description of the method of using these may

be helpful in pointing out some of the errors and means of correcting them. Several other

forms of capillary tube viscometers are described and instructions for their use published

in the appendix of ASTM Method D 445 [6]

and still other types or forms will be found in

the literature.

Perhaps the simplest form is the straighttube pipet viscometer, which closely resembles

the ordinary transfer pipet modified to provide

a capillary tube below the bulb and two fiducial

lines, one above and one below the bulb. The

instrument may be mounted in a vertical position in a thermostat with the lower end extending through the bottom of the bath. The instrument is filled to a point somewhat above the

upper fiducial line by holding the sample container below with the viscometer tip submerged

and applying suction to the top. The liquid is

held in the viscometer by closing one end for

awhile to allow it to come to test temperature,

then opening the end and allowing the liquid to

flow from the instrument, observing the time

for the meniscus to fall from the upper to the

Committee which through a cooperative test

program checks the viscosity values determined

by the commercial laboratory. NBS has had

representation on the API or ASTM committees for most of the time since inception of the

program. During this period the requirements

for precision and accuracy of viscosity measurements have grown more exacting, along

with a more widespread understanding of the

means by which greater precision in measurements can be achieved.

The present series of ASTM oils was designed to meet the needs of petroleum testing

laboratories, particularly with respect to the

information supplied with the samples. It is ex- pected that some slight modification and extension of the series and amplification of the data

reported, for each oil will result in a series of

calibrating oils which will meet the needs of

laboratories in other industries and may make

possible discontinuance of the NBS series.

Tube Viscometers

lower mark. The glue-type viscosity pipet,

figure la, is a special form wi+h a relatively

large diameter tube above the bulb and a funnel

top. In using this instrument, the sample is

preheated to slightly above test temperature

before pouring into the viscometer. The lower

end is closed with a finger and the temperature

of the sample may be checked with a thermometer inserted through the large upper tube.

The thermometer must be removed before starting the run. Various other modifications of the straighttube pipette viscometer have been used, but the

most widely used glass capillary tube viscometers are of the Ostwald U-tube type or modifications of it. The Ostwald instrument, figure lb,

is charged with a known amount of liquid,-

either by use of a suitably calibrated pipet or by weighing the instrument (or pipet) before

and after charging the instrument or by filling

to a mark on the large tube 1. To operate,

pressure is applied to tube 1 or suction to tube

2 to cause the liquid to rise in the left limb to a point slightly above line a. The pressure (or

suction) is released and the time for the meniscus to pass from a to 6 is observed. The measurement may be repeated at the same or diff"erent temperatures without refilling the instrument.

7
(b) OSTWALD

(a) STRAIGHT-TUBE (GLUE TYPE)

I 2

/ \

r

c

(d ) CANNON MASTER

(e) SIL (f ) UBBELOHDE

SUSPENDED LEVEL

(g) REVERSE FLOW

FOR OPAQUE LIQUIDS

Figure 1. Representative types of capillary tube viscometers.

Obviously the hydrostatic head causing flowis dependent upon the volume of the charge at

the test temperature and for any given filling

will vary with the temperature of test. One

modification (not shown) of this instrument

has a filling mark on tube 1 just above bulb B

and bulbs A and B are cylindrical with conical

ends.

The Cannon-Fenske and the Cannon Master

viscometers, figures Ic and Id, have auxiliary

bulbs D above the fiducial bulb A. The capacity

of the instrument above the line b serves to

measure accurately the volume of charge at

ambient temperature. This is accomplished by

inverting the instrument, dipping the end of

tube 2 in the sample and applying suction to

tube 1, drawing the liquid into tube 2 to a

point somewhat beyond b, raising the instrument from the sample, and quickly closing tube

2 with a finger, taking care to avoid drawing

8
air into tube 2 before closing it. Suction is

released and excess liquid removed by easing

the finger pressure, then turning the instrument right-side-up and removing the finger

with a wiping action to prevent excess liquid

on the finger and top of tube 2 from draining

into the instrument. After charging, the instrument is placed in the thermostat and the charge

allowed to drain down into bulb B. Thereafter,

operation is the same as for the Ostwald viscometer.

The SIL viscometer, figure le, provides for

measuring the volume of charge at the test

temperature. This is accomplished by drawing

the top of bulb 5 to a moderately small diameter

and providing a gallery around it. The liquid

is poured into tube 1 while the instrument is

inclined about 30° from the vertical. Enough

liquid is added to fill the lower part of the

instrument and the gallery to a point somewhat

above the top of bulb B, taking care to avoid

trapping air in the tube between B and the

capillary. After the instrument has been in the

thermostat a sufficient time for it to come to

temperature, the excess liquid is withdrawn by

applying suction to tube 3. Thereafter operation is the same as for the Ostwald instrument.

Repeat observations may be made on the same

specimen at the same or successively higher

temperatures, at each new temperature allowing time for adjustment of the working volume

by overflow into the gallery.

The Ubbelohde suspended level viscometer,

figure If, is charged by pouring the liquid into

tube 1 while the instrument is inclined about

30° from the vertical. When returned to a

vertical position and the liquid drained from

tube 1, the instrument should be filled to a level

between the two lines on bulb B. To operate,

tube 3 is closed with a finger and suction

applied to tube 2, drawing the liquid into bulbs

C and A and half filling the small bulb above

A. The suction is released, tube 3 opened, and

tube 2 closed immediately with the finger until

air entering tube 3 fills bulb C. Tube 2 is then

opened and the time observed for the meniscus

to pass from a to h. Repeat determinations

may be made on the same specimen at the same

or different temperatures.

Other modifications of the U-tube instrument

include several such as shown at figure Ig,

designed for use with opaque liquids. In general, these place the fiducial bulb low in one

limb and the capillary with a reservoir bulb

above it in the other limb. Various methods,

depending upon the detail designs of the instruments, are used to measure the volume of

charge. The instrument shown at figure Ig is

intended to be filled in a manner similar to that

used with the Cannon-Fenske and the Cannon

Master instruments. After charging, the liquid

is restrained from entering the fiducial bulb by

closing one limb with a rubber tube and pinch

clamp until the test temperature is attained. In

these instruments the time to fill the fiducial

bulb is observed. In one form, the sample flows

from the reservoir bulb by siphon action which

is started when desired by applying suction to

the limb containing the fiducial bulb. These

instruments for opaque liquids must be cleaned

and refilled for repeat measurements, except

that one form provides two fiducial bulbs, one

above the other, so that the flow is divided into

two parts which may be timed separately, thus

getting a check measurement with one filling.

6. Calibration of Relative Capillary Tube Viscometers

_ For all the instruments mentioned as illustrative of relative capillary tube viscometers, the

pressure causing flow is due to the difference

between the levels of the free surfaces of the

liquid, i.e., P=pgh where g is the acceleration

of gravity and h the mean effective difference

between the levels of the liquid surfaces. With

this substitution for P, eq (4) becomes

TT pgh tH rtipV

^V{1 + nr) ~S7r (I + nr)t

(5)

Neglecting minor corrections to be discussed

later and with certain reservations as to operating conditions and techniques, the quantities

g, h, r, V, and I are constant for a given instrument. The value of n is somewhat uncertain

but, based on theory supported by some experimental evidence, is usually considered to be

near unity or smaller so that in instruments

with reasonably high ratios of l/r, the quantity

(I + nr) may be considered constant or substantially so, even though n may vary somewhat for different rates of flow. With these

considerations we may now write

in which

C =

1

P

-rrghr*

V = Ct — mB

(6)

8F(Z + nr)

and B V

87r(Z -I- nr)

and V is kinematic viscosity.

Often these instruments are used under conditions such that the kinetic energy correction

is negligibly small in comparison with Ct and

eq (6) becomes

V = ct. (7)

If a suitable liquid for which v is known is

available, the value of C in eq (7) may be de9
termined by observing the flow time, t, for this

liquid and dividing v by t. When an instrument is used under conditions

such that the kinetic energy term is not negligible, but still small, mB may be considered a

constant, following the same reasoning as was

used for the quantity nr. Calibration of the instrument for such use requires that two calibrating liquids be available and the flow time

for each be determined. The known quantities,

V, and t, for each liquid are inserted in eq (6)

and the two equations solved simultaneously.

This gives the relations

C =

^ete Vftf

and

mB —

te tf

1^

in which the subscripts e and / refer to values

associated with calibrating liquids e and /, re- spectively. However, since the correction is

small, V is approximately proportional to t and

the difference between the two ratios in the

numerator of the expression for mB will be

small and influenced unduly by minor errors and uncertainties in the values for v and t. Thus the expression affords a poor measure of

the value of mB. A more satisfactory evaluation of mB may result from assuming that

m=l and n = 0, then calculating B from the

dimensions of the instrument and the ex- pression

B =

V

S-n-il + nr)

Then the value of C may be determined using

eq (6) and data for a calibrating liquid having

a reasonably high flow time, i.e., a liquid for

which mB/t is very small in relation to Ct.

Cannon et al. [7] propose the following relation to replace eq (6)

:

(8)

, 0.001667^ ^, , , where E = . They recommend that

HCry

E be determined experimentally rather than

calculated from this expression. On the basis

of their work with various instruments, some

of special design, they concluded that "E is a

constant over the important Reynolds number

range."^

During calibration, all details of filling and

operation should be the same as will be used

subsequently in determining the viscosity of an

unknown liquid.

Considering the definitions of C and B,

ghr*

8Vil + nr)

and B =

V

Siril + nr)

it is obvious that these are constants only for

certain conditions since the dimensions r, V,

and I will change with temperature; g varies

with location; and h varies with temperature,

the vertical alinement of the instrument, and,

in some instruments, with the volume of liquid

in the instrument. The pressure difference

available to cause flow is also affected by the

surface tension of the liquid and the density of

the air column in the instrument, or of the

ambient air in the case of straight-tube instruments which extend through the thermostat.

Also, the temperature and hence the viscosity

of the liquid may be expected to vary throughout the volume of liquid in the capillary due to

the heating effect mentioned above, and the appropriate value of V may vary due to incomplete drainage from the fiducial bulb.

Apparently many workers assume that it is

necessary to calibrate these instruments at each

temperature at which they will be used. This

is not the case. The effects of thermal expansion on the instruments are largely self-compensating. Any substantial adjustment of the

calibration constant as is required with some

U-tube instruments when used at different temperatures is due primarily to expansion of the

liquid rather than the instrument. Thus, even

with an instrument calibrated at the temperature of test, a correction will be required for

the difference in thermal expansion between the

calibrating and the test liquid.

The following detailed consideration of the

various factors mentioned should lead to a

better understanding and if desirable to improved precision and accuracy in measurements

of viscosity.

6.1. Variation in Value of g

It is obvious that for any given instrument,

other factors being the same, the value of C

appropriate for use at different geographic

locations varies directly with the acceleration

due to gravity at the various locations, so that

if an instrument is calibrated in one laboratory

They consider this range to be from 80 to 500 "because all liquid viscosity measurements in present day viscometers that re- quire a significant kinetic energy correction fall within this range."

10
and used in another, the value of C should be

adjusted by the relation

C„==-^Cc (9)

9c

in which the subscripts c and u indicate, re- spectively, the values for the calibrating laboratory and the laboratory where used. The cor- rection usually will be small, but should not be

overlooked since it may be significant. For

example, a correction of about 0.15 percent

would be required between Seattle, Wash., and

El Paso or Austin, Tex.

6.2. Curvature of the Capillary

All the viscometers in figure 1 have capillaries which are straight. In order to provide

instruments of convenient size but having the

advantages of a long tube, the suggestion is

made from time to time that this be accomplished by bending the capillary, either by ex- tending it around the U-bend in the U-tube

instruments or forming it into a helix or otherwise. A few instruments with one or two Ubends in the capillary are in use. Several

workers have investigated the flow through

bent capillaries and curved pipes. The results

of this work, both theoretical and experimental,

confirm what might be surmised, that the radial

acceleration involved in deflecting the flowing

liquid from a straight course disturbs the

normal flow pattern and velocity distribution

of a straight tube and results in an abnormally

high pressure gradient in the curved section.

This in itself might not be significant in a relative instrument, since we rely on the calibration

with a liquid of known viscosity to yield a

properly weighted integration of the effects of

variations in bore size and shape, effective

length, etc. However, experimental results have

indicated that the range of flow conditions in

which the flow time is proportional to the viscosity, i.e., conditions for which the equation

v=Ct is valid, is restricted when the capillary

is curved. Thus bending the capillary tends to

defeat the purpose of this design feature and,

in general, it appears desirable to use straight

capillaries and to make necessary bends only in

tubing having an inside diameter several times

larger than that of the capillary.

6.3. Heating Effect

In capillary tube viscometers used under conditions such that the kinetic energy correction

is negligible, the mean temperature rise at the

exit of the tube assuming adiabatic conditions

is AT °C = 2.34X10-^ h/c where c is the specific

heat of the liquid. At the entrance to the capillary, aT=0 and the mean temperature increase

for the whole tube is of the order of AT— 1.17

XIQ-^ h/c. For instruments of the types shown

in figure 1 the value of h varies from about 10

to 50 cm. Taking 0.4 as a representative value

for c for petroleum oils and many liquids,

AT = 0.0003 to 0.0015 °C.

If external pressure is applied, an additional

increase in the mean temperature of Ar= 0.0003

°C per 10 cm water pressure is possible.

Usually the heating effects will not be significant with instruments of the types shown in

figure 1. The above formula is intended only to

indicate the possible magnitude of the mean

temperature rise and should not be used for

correcting measurements made under high

shear rate conditions because it does not take

into account the temperature gradients along

the tube and across the stream which will distort the theoretical parabolic distribution of

velocities, nor the heat loss to the walls of the

capillary and the thermostat.

6.4. Drainage Error and Use of

External Pressure

Use of eq (5) in connection with viscometers

such as those shown in figure 1, except Ig, as- sumes that the volume of liquid, V, flowing

from the fiducial bulb will be the same for

liquids having different viscosities. A number

of investigations of the validity of this assumption have been made using various techniques.

Experiments in this laboratory confirm the

findings of some others that, if the rates of

flow from the fiducial bulb are proportional to

the kinematic viscosities of the liquids, the

volume delivered by the bulb is a constant at

least for a wide range of viscosities. Consequently, if the instruments shown in figure 1 are used under conditions such that eq (7) is

applicable or the value of mB/t in eq (6) is

quite small, we may assume that F is a constant

although differing from the capacity of the

bulb, and that there is no appreciable drainage

error in the normal use of the instruments.

However, if the instruments are used with

additional air pressure to increase the rate of

flow either to extend the range of the instrument or to test the Newtonian character of the

liquid, the magnitude of the drainage error must be determined and a correction applied

unless the flow is into a clean dry fiducial bulb

as might be the case with an instrument such

as that shown in figure Ig.

If necessary, the drainage error may be estimated from data obtained by determining the

volume of the liquid remaining in a bulb of as nearly as possible the same size and shape as

the fiducial bulb, when it is allowed to empty at

different rates. The correction factor to ac- count for the reduced volume of flow would be

the ratio V/Vp, i.e., the ratio of the volume discharged at the normal rate to the volume discharged at the rate observed when additional

\ 11
pressure is used. It is assumed that this ratio

would be the same for two bulbs of about the

same size and shape and at the same flow rates.

This correction factor should be applied to the

observed flow time for the liquid.

For instruments of the Ostwald type (figs,

lb, Ic, Id, and le) the excess liquid remaining

on the walls of the fiducial bulb would cause

the lower liquid surface to rise more slowly

than normal, resulting in a slightly higher than

normal mean effective pressure head. An approximate estimate of the correction factor for

V~Vp

this effect is 1+ where R is the estiTrR-h

mated mean radius of liquid surface in the

receiving bulb and h is the normal liquid head.

This factor is applied to the instrument con- stant C, as is the factor H/'h needed to account

for the direct effects of the increased pressure.

In this factor, H is the total pressure causing

flow, i.e., normal head, h, plus the applied pres- sure expressed as a column of the test liquid.

All three corrections may be required.

A somewhat inverse situation occurs in the

normal use of these instruments when the

liquid is forced or drawn up to fill bulb A. If

this is done more rapidly than normal, a slight error in the initial head may result from imperfect drainage in bulb B. Although the error due to this may be quite small, it may be minimized by always using the same pressure or vacuum to fill bulb A so that the flow times

from bulb B will be approximately proportional

to the kinematic viscosity of the liquids.

6.5. Alinement

The vertical distance, h, between the two

free liquid surfaces is altered if the axis of the

instrument is not vertical. The axis of a capillary tube viscometer may be defined in different

ways, but for the purpose of this discussion it is taken to coincide with the vertical line

through the center of the upper bulb when the

instrument is calibrated. To avoid error due to

misalinement, it is usual either to adjust the

position of the instrument carefully each time

it is used or, preferably, to provide a suitable

clamp or holder, or a fixture permanently attached to the instrument which will automatically position the instrument the same each

time it is used. The latter procedure, of course,

requires that the thermostat cover or other

support for the instrument be not easily displaced and that its preferred position be easily

checked with a level or plumb line.

For instruments of the type shown in figures

la, Ic, and If, the axis normally passes through

the centers of the two liquid surfaces. Misalinement of the instrument, so that its axis deviates

from vertical by an angle 9, reduces the effective head by the amount (1 — cos 9) . For these

instruments the change in effective head and

the error in the viscosity measurement will not

exceed 0.1 percent if 9 does not exceed 2"34'.

For instruments shown in figures lb. Id, le,

and Ig, the center of the lower surface is displaced by a hoi'izontal distance d from the axis

of the instrument and an additional change in

h of ±d sin 9 may result from misalinement so that the total error may be (1 — cos 9)h ± d sin

9 or /i(l-cos 9 ± d/h sin 9). If 0 = 2^34' the

additional error in h could be as much as ±0.0447rf. The percentage error would depend

to some extent on the ratio d/h. If d/h — 1/10

and 6' = 2"34', the total error could be as great

as -t-0.35 percent or —0.55 percent. The maximum error occurs when the plane of the instrument lies in the plane of the angle 9 and

the error could be 0.1 percent if ^ = 0°33'.

Actually, the d/h ratios for some of the recognized instruments of this type is lower than

1: 10 and alinement is more critical than in this

example.

The precisely correct alinement of an instrument is that used during calibration, hence it appears probable that closer reproduction of

the calibration alinement will be obtained when

the instrument is calibrated by the user. If the

user's equipment does not provide reproducible

alinement, his viscosity measurements will not

be reproducible. This would not be corrected or improved by calibration in another laboratory where reproducible alinement, possibly on

a somewhat different axis, may be available.

6.6. Effect of Thermal Expansion

of the Instrument

1

5

If an instrument is calibrated at a temperature Tc and used at a temperature Tu each

linear dimension is increased by a factor F = l

+ eiTu — Tc) , where e is the mean linear coefficient of thermal expansion of the material of ;i which the instrument is constructed. The capac

ity or volume of the fiducial bulb may be con

sidered as the product of three linear dimen

sions ; hence V would be increased by the factor

F'\ Indicating these changes in the definitions

of C and B, we have

Cu = -

and

Bu =

-rrghr*

SV F^ {IF + nrF) 8V (Z + nr)

F = CcF

VF' V

F- = BcF-.

STrilF + nrF) SV{l + nr)

Hence C„ = [1 + e(T„ - T,)]Cc and 5„ =

[1 + f(r„ — Tc)]-Bc. These instruments are

usually made of thermal shock resistant glass !; and the value of e is of the order of SXIO"*^ per ^ degree C. If Tu-Tc = 100 Celsius degrees, F is

12
approximately 1.0003, e.g., the appropriate

value of C for use at a temperature 100° above

or below the calibration temperature would be

only 0.03 percent higher or lower than the value

at the calibration temperature. The change in

the value of B would be approximately twice

this amount, but this probably would have

no significant effect on the viscosity determination since the correction term containing B is

small or negligible. In other words, for ex- ample, if an instrument is calibrated at 25 °C

(77 °F) and used at any temperature in the

range from -75 to +125 °C(-103 to +257

°F) neglecting the correction for the thermal

expansion of the instrument would result in a maximum error of only about 0.03 percent.

Discussion of the above factors is intended to

call attention to possible errors which can be

avoided or minimized, rather than to develop

correction factors or formulas, although some

were given. The following four corrections

relate to adjusting the value of C to compensate

for differences between test conditions and the

standard reference conditions for which the

unadjusted value of C is appropriate. Since the

effect of these differences may be expressed in

terms of hydrostatic head of the test liquid, it

is convenient to compute the corrections as

fractions of the head, h. Then the algebraic

sum of the fractions increased by one provides

a single correction factor for h which may be

applied to C, since /i is a factor of C. It should

be noted that since h does not appear in the

kinetic energy term, these corrections do not

apply to it.

6.7. Correction for Temperature of Filling

In instruments shown in figures la, le, and

If, the effective volume of liquid is adjusted

for each run and the temperature at which the

instrument was filled is not critical. With

instruments shown in figures Ic, Id, and Ig,

the volume of charge is measured at ambient

temperature, which in most laboratories is a

variable. As a result, the actual volume of

I charge at a given test temperature is variable.

jThis affects the value of h and hence of C, so that some adjustment of the value of C or cor- rection of the observed time of flow must be

made to compensate for the changes in h. With

the Ostwald viscometer, figure lb, the quantity

of liquid charged can be adjusted so that h

will be a constant, but probably it is more common practice to introduce a fixed volume of

charge measured at ambient temperature, in

which case a correction for filling temperature

lis required.

To calculate the correction for filling temperature, temperature of test, air column correction, and surface tension effects, it is con- venient to assume some set of standard conditions as a common basis for the calibration and

use of the instrument. We have based the calibration constants for our viscometers on the

assumption that they were filled and calibrated

with water at 20 °C. That these conditions are

hypothetical for the instruments with the larger

capillaries, which are entirely unsuitable for

calibration with water, is immaterial, since the

assumption serves only to provide fixed refer- ence conditions.

The capacity of the instrument to the filling

mark at the standard temperature, Tc, is V c- This is the correct volume of charge. The

capacity at the filling temperature Ti is Vi=Vc

[l + ^iT^ — Tc)], which is the measured volume

of charge. j3 is the mean volume coefficient of

thermal expansion of the glass of which the

instrument is constructed. The volume of the

charge V,. at Tc when filled at Ti is

l+fi{Tr-To) . , . , ... V s=V c in which is the mean

volume coefficient of thermal expansion of the

liquid in the temperature interval Ti — Tc, i.e.,

Pi

The error in the volume of charge is c—S/ s and, assuming that T^>Tc for any given position of the upper meniscus, the lower meniscus

will be lower than normal by ——— where R

ttR'

is the radius of the lower meniscus.'' Consequently, the value of h is increased to

hu = h +

ttR^

The fractional change in h due to filling at

instead of Tc is

hu — h Vc—Vi

h rR'h

Substituting for V s and simplifying, we have

(see footnote 6)

V,

7rR-h

{a, - p) (r, - Tc)

1 + a, {T, - Tc)

. (10)

It may be noted that is a constant for

TrR'h

any given instrument, also, that usually the

expression for X^ may be simplified to read

" For the reverse flow type instrument, figure 1 (g) , this correction has the opposite sign, since for any given position of the lower meniscus, the upper meniscus will be lower and the value of h

decreased.

13
X = (10a)

without introducing appreciable error. For the purpose of estimating this and other

corrections, appropriate values for Vc, h, and R

may be obtained as follows:

The value of Vc may be determined by filling

bulbs A and D and tube 2 with water or mercury and weighing the quantity discharged or with somewhat less precision by use of a buret

to determine the volume of water required to

fill these parts of the instrument. To accomplish

the first method, a glass stopcock is attached to

tube 2 with transparent tubing. The tube on

the other side of the cock should be drawn

down to form a fairly small tip similar to those

on burets. With the instrument in the inverted

position, liquid is drawn or forced through the

cock to fill the instrument to a point in the

capillary. By careful manipulation of the cock,

the liquid is drawn down to the fiducial mark 6

above the bulb (instrument inverted) and then

the contents of the instrument drawn into a

tared container and weighed. In the second

method, the instrument is clamped in the inverted position adjacent to a standard calibrated buret, the tip of the buret connected to

tube 2 with trasparent tubing, and the viscometer filled with liquid from the buret, noting the

difference between the buret readings when the

liquid just enters tube 2 and when the viscometer is filled exactly to mark h. An approximate value for h may be taken as the head at mean time, i.e., the difference in

level of the two liquid surfaces in the instrument when half the flow time for that liquid

has passed. A highly accurate value for h is

not required since it enters into calculations of

correction terms which are small.

The value of R may be estimated from the

outside diameter of the bulb corrected for the

estimated wall thickness, or the instrument

may be filled in the normal way, the liquid

drawn up to line a, and the level in bulb B

marked accurately. Then allow the liquid to

drain down to h and mark the level in B.

R= where V is the capacity of bulb A,

and S is the distance between the two marks on

B. {V may be determined by an adaptation of

one of the methods suggested for determining

Vc) . A more precise method, and one which will

give some indication of the uniformity of R at

different levels in B, is to plug the U-bend with

wax, mount the instrument firmly in a vertical

position and fill bulb i> to a point slightly below

the initial level, measure the height of the

liquid surface above some reference point with

a cathetometer (or measure the depth of the

surface below the top of the instrument with a micrometer depth gage) , add a known small

increment of liquid, and again measure the'

height of the surface. This is repeated until B

is filled somewhat above the final level. The

mean value of Ri for the region filled by eachi

increment is Ri = -, where Vi is the volume

of the increment and Si is the change in level

of the surface resulting from the addition of

the increment. This method assumes that the

shape of the meniscus is constant as would be

the case if the portion of the bulb B involved is

cylindrical.

6.8. Correction for Temperature of Run

As shown above, when these instruments are used at a temperature other than that at which

calibrated, thermal expansion of the instrument

results in a slight change in the values of the

constants C and B, but usually the changes are small enough that they may be ignored,

although calculation of an appropriate correction is not difficult. However, in the U-tube

type instruments in which the effective volume

of charge is not adjusted at the test temperature, thermal expansion of the liquid will

change the effective value of h and significant

corrections may be necessary.

Assuming that the instrument has been filled

at Tc or a correction made for filling at another

temperature, the apparent change in volume of

charge between Tc and the test temperature,

Tu, is

S/^-Vc^ Vcil+ {au- /3){T.-Tc)'\ = Vc(au - 13) (Tu - Tc),

where is the apparent volume of charge at

T

The value of h will be reduced^ by — -\ ttR'

f due to thermal expansion of the liquid. This is^

only partially compensated by the cubic expansion of the instrument and by e{Tu — Tc)h due

to linear thermal expansion of the instrument.^ j Then the effective value of h at the test temperature is

I

hu = h- ZlZ^ + e{Tu- Tc)h.

ttR' j;

Letting Xu be the fractional change in h, we!

'For the reverse flow type instrument, figure (1 g) , h is increased 1 by expansion of the liquid and linear expansion of the instrument I but decreased by the cubic expansion of the instrument. '

* The cubic expansion of the instrument reduces the effect of ex- i pansion of the liquid and thus tends to increase h; also, the linear

| expansion of the instrument tends to increase the value of h. This may appear to be making a double correction for expansion of the ^ instrument. However, the point may be clearer if we consider the ; case of an instrument charged with a hypothetical liquid having the same volume coefficient of thermal expansion as the instrument: a

' change in temperature would produce no apparent change in the , volume of the liquid, but the distance between the two liquid surfaces, h, would change in accordance with the change in tempera- 1 ture and the linear coefficient of thermal expansion of the glass.

j

14
write

Xu —

Xu —

hu — h V,

h rR-h

+ e{Tu- Tc)

(uu — 13) — e (Tu-Te).

(11)

6.9. Air Column Correction

In developing eq (5) from eq (4) we said

that P = pgh. This neglected the hydrostatic

head of air in the other limb of the instrument

(or the ambient air in the case of a straighttube pipet viscometer). The correct expression for P is

P = (pwc ^ Pac) Qh,

where pac is the density of the air in the instrument (or the ambient air when a straight-tube

instrument is used)

.

To correct the kinematic eqs (6) and (7) for

this, we must multiply the constant C by 1 —

Then under calibration conditions (real or

Pwc hypothetical)

Pwc

and under test conditions,

(i ~ —

SVl Plu

where pac and p„,c are the density of air and

water at 20 °C, respectively, and pa,,. and piu are

the density of air and the test liquid at the test

temperature. Thus the geometric head, h, is

reduced by the factor 1 — under calibraPwc

tion conditions and by the factor 1 — under

Plu

test conditions. The fractional change in head is

Xa =

Pac

\ Plu I \

Pac

Pwc)

hil

Pac

Pwc

pivc

Pau

plu ,

Pwc

Pwc Pac (12)

The precise values for pac and pau will vary

with barometric pressure and humidity but

the value of Xa is small and use of reasonable

average values will not involve serious error. We use values for the density of air at 760 mm

of Hg pressure having a dew point of about

15 °C. Thus Pac = 0.001197 g/cm\ The density

of water at 20 °C is 0.99821 g/cm\ Using

these values,

Xa = 0.001200 - 1.0012 (12a)

Plu

6.10. Correction for Surface Tension Effects

Considering the effects of surface tension in

a capillary tube viscometer in terms of capillary

rise, the driving head is reduced by the capillary rise in the upper bulb and increased by

the capillary rise in the lower bulb. Usually the

diameters of the bulbs are fairly large and the

capillary rise is small except near the fiducial

marks. Fortunately the relatively large capillary rise when the liquid surface is near the

fiducial marks is effective for only a small

fraction of the total flow time.

Instruments (e) and (f) of figure 1 are intended to minimize the effects of surface tension so that they may be used with liquids with

widely different values for y without requiring

correction. This requires proper matching of

the two bulbs connected to the opposite ends of

the capillary. Obviously, other instruments

shown in figure 1, except the glue type, could

be rendered less sensitive to surface tension

effects if proper consideration were given to

matching the surface tension effects in bulbs A

and B.

Accurate evaluation of the effect of surface

tension in altering the mean effective head, h,

is difficult because of changing diameters of

the liquid surfaces, changing inclination of the

bulb walls as flow progresses, and the fact that

the simple capillary rise formula, hy =

pgr'

IS

applicable only to tubes with vertical walls and

which are literally capillary in size. The effect

usually is small and often it is ignored or a

correction applied which is only a rough approximation based on the simple capillary rise

formula and estimated mean effective diameters

for the bulbs. These procedures may be satisfactory when the instrument is used only with

liquids having surface tensions approximately

the same as that of the calibrating liquid or when accurate values for viscosity are not re- quired.

A reasonably accurate evaluation of the cor- rection required for a given viscometer and

liquid may be made either by calculation or by

experiment. Both methods are somewhat

tedious.

To estimate the correction by calculation, an

accurate vertical profile sketch or photographic

silhouette of the interior surface of the bulb is

15
made and divided into a number of horizontal zones (perpendicular to the axis of the instrument). The lengths of these zone boundaries

and the angle ^ between the axis and the normal

to the profile at each intersection of the profile

and zone boundaries are measured. The angle 4> is between the normal and the segment of the

bulb axis below its intersection with the normal.

The measurements give the diameter of the bulb

at each zone boundary and the angle ^ for use with the tables prepared by Bashforth and

Adams [8] to obtain values for a quantity b

and the volume of the meniscus'-^ at each zone

boundary.

The capillary rise at each boundary is hyb ~

Or ^ —, where a- = —. If the zones are narrow, the

b pg

value of hy~ for the zone may be taken as the

arithmetic mean of the values for hy^ at the

upper and lower boundaries. The time during

which the mean value, hy^, for each zone is

effective is proportional to the volume of flow

and inversely proportional to the mean effective

head, h~, for the zone. The vomme of flow is

estimated as the volume of the frustrum of a cone (with radii and height equal to those of

the zone) decreased by the volume of the meniscus at the upper boundary and increased by the

volume of the meniscus at the lower boundary.

(For this purpose, the meniscus at a boundary

is the meniscus which is tangent to the bulb

profile at the boundary—not the meniscus

tangent to the zone boundary.) The mean effective head for each zone may be taken as the

mean geometric head for the zone /i,,- increased

by the capillary rise in the lower bulb hys and

decreased by the mean capillary rise for the

zone hyz, i.e., /i^ = hg^ + hys — hy~. Then, if

Vz, hy~, and h~ are, respectively, the volume of

flow, the mean capillary rise, and the mean effective head for each zone, the total effective

capillary rise is

V.hyz

hy =

Use of this method is limited by the range of

the Bashforth and Adams tables.

In the experimental method of estimating hy, a bulb with two fiducial lines, of the same size

and shape as the fiducial bulb of the instrument,

is connected to a vertical cylindrical tube of

known diameter by a U-shaped glass or flexible

connection and mounted in a stirred bath to

prevent rapid changes in temperature. The Ushaped connection is filled to the lower fiducial

' The volume of the meniscus is the volume enclosed by the meniscus and the horizontal plane containing the line of tangency

between the meniscus and the tube or bulb which is assumed to be symmetrical about its vertical axis.

16

line with water or other liquid of known sur-i

face tension and the heights of the menisci in

the two arms referred to some common refer- ence level are measured with a cathetometer

or equivalent means. A known volume of the

liquid is added to the cylindrical tube and the

change in the levels of the menisci measured.

This is repeated until the fiducial bulb has been

filled to the upper fiducial line. The work can

be carried out at ambient temperatures provided these do not vary greatly or rapidly. By

observing the bath temperature when measuring each pair of meniscus heights, suitable

corrections for changes in volume may be made,

if necessary. Then if Vi is the volume of the

increment, R the radius of the cylindrical tube,

and A/i,. the change in level in the cylindrical!

tube, the volume of liquid entering the bulb is|

Vz — Vi — ttR- Ahr. The capillary rise in the|

fiducial bulb for any pair of observations of thei

menisci heights is equal to the calculated capil-|

lary rise in the tube, hyr, plus the observed level

of the meniscus in the bulb and minus the observed level of the meniscus in the tube. If thei

values of V~ are small, the arithmetic mean;

value of the capillary rise in the bulb before i and after adding the increment may be taken]

as the mean effective value, hy^, for the portion]

of the increment entering the bulb, V^. Then,

h

Ah + Ahi

yz + hyTy

where Ah and Ahi are the differences between

the liquid levels before and after adding the increment. The differences must be taken by subtracting the level in the tube from the level in

the bulb and may be either positive or negative,

j The diameter of the cylindrical tube will be too

large for use of the simple capillary rise formu-

'

la and hyr must be computed by use of the Bash-

,

forth and Adams tables [8] or by use of Sug1

den's table [9] . I The mean effective value of the capillary rise i for the whole bulb is

hy

Vz hyg

hz

where h~ is the mean effective geometric head i for any increment of liquid V~, calculated as

j though the bulb were actually the fiducial bulb \ of the viscometer. Thus, if h is the head at

'

mean time for the viscometer and e is the disj tance from the upper liquid level at mean time

to the lower fiducial mark, I

I

h:: = {h — e) -\- J, \

where J is the height of the midpoint of the
zone above the lower fiducial line of the ex- perimental bulb.

If this method is applied directly to the viscometer rather than to a separate bulb closely

resembling the fiducial bulb of the viscometer,

considerable time must be allowed after each

addition of liquid to permit the system to reach

equilibrium before reading the levels of the

menisci.

An inherent error in this empirical method

when using a cathetometer results from differ- ences in the optical path at different levels due

to differences in the angles of incidence and in

the wall thickness of the bulb. This can be

minimized by using a test liquid and bath liquid

having approximately the same refractive index as the glass of the instrument. The value

of hy thus determined is for the capillary rise

in the fiducial bulb. The capillary rise in the

receiving bulb may be estimated in a similar

manner or, if this bulb is cylindrical, the capillary rise may be estimated by use of Sugden's

table [9]. The driving head in the instrument

corrected for surface tension effects is ^ —

hyp + hyu where the subscripts f and r indicate the values for the fiducial bulb and the

receiving bulb, respectively.

It may be noted that both methods for estimating the surface tension effects are based on

static conditions and neglect the effects of distortion of the menisci when in motion. A re- ceding meniscus has a smaller than normal

radius of curvature and exhibits a greater than

normal surface tension effect. The converse is

true for an advancing meniscus. Hence in a kinematic viscometer the motion of the liquid

tends to augment the surface tension effect in

the upper bulb and to diminish it in the lower

bulb, (It is assumed that the liquid wets the

walls of the instrument, otherwise the effects

of the moving menisci would be opposite to

what has just been stated.) In ordinary kinematic viscometers, the motions of the menisci

are quite slow except for brief periods at the

beginning and end of a determination and it is

believed that the distortion of the menisci can

be of only academic interest. This effect was

neglected also in the discussion of the use of

external pressure, although in some instances

when considerable external pressure is used

with a viscous liquid the distortion of the

menisci may be quite noticeable. Nevertheless,

the error due to neglecting this effect may well

be negligible, since the whole effect of surface

tension would be relatively small in relation to

the applied pressure.

The fractional change in the effective value

of h due to changing from the the standard

reference conditions to the test conditions is

Xy =

~ ^\ (13)

h

where hyc and hy,, are the net effective capillary

rise of the calibrating and test liquids, respectively.

On the basis of results of experimental determination of the capillary rise effect for

water and three hydrocarbon liquids in an ex- perimental bulb similar to the essentially

spherical fiducial bulbs of our water-calibrated

Cannon Master viscometers and calculations of

the capillary rise effect for water in these

instruments using Bashforth and Adams tables,

we have found that for our Cannon Master

viscometers,

0.1235 - 0.8346a^

Xy = (14)

. h

or, since h — 46.4 for the Cannon Master viscometers,

Xy = 0.00266 - O.OlSOa^ (15)

Calculations of the capillary rise effect with

water and three hypothetical liquids in one of

our Cannon Master viscometers having a somewhat elongated fiducial bulb indicated that the

same relation was a reasonable approximation

for this shape bulb and we have used eq (15)

for all our Cannon Master viscometers.

These four corrections or adjustments are intended to account for differences in the

pressure causing flow, which result from differ- ences between conditions of calibration and use. They have been computed as actual or equivalent fractional changes in h. We do not attempt to measure h accurately and the cor- rections may be smaller than the uncertainty in

h. This is not particularly significant since h is a factor in determining the value of C, which

is known (or to be determined) accurately and

thus involves an accurate but undetermined

value for h. In effect, this accurate but un- determined value for h may be corrected by

applying the correction to C. This may be ac- complished conveniently by adding the fractional correction to unity to obtain a combined

correction factor or multiplier, M, to be applied

to C, i.e.,

M = 1 + + X„ + + Xy. (16)

Then eqs (6), (7), and (8) become

v = CMt- — \l + e{Tu- Tc)y', (17)

v = CMt; (18)

E[l + s{Tu- Tc)y

V = CMt - — — —. (19)

The kinetic energy term does not involve

17
pressure and is unaffected by the pressure adjustments effected by use of the factor M.

However, as noted above, a correction for thermal expansion of the instrument may be appHed, although the effect probably would have

no significance. The effects of thermal ex- pansion of the instrument on the value of C

are included in the Xu correction.

To calibrate an instrument it is necessary to

observe the flow time of water or some liquid

of known viscosity and to compute the various

corrections X^, Xu, etc. Then if conditions are such that the kinetic energy correction is negligible, i.e., the Reynolds number does not exceed a value of 10 to 15, v = CMt and C = —

Mt

If the kinetic energy term is not negligible,

it will be necessary to determine the flow times

and correction factors for two liquids, e and /,

of known viscosity and solve one of the following pairs of simultaneous equations:

(mB)

(a) Ve = CMete "

(mB)

vf = CMftf

or E

(b) Ve = CMete "

te' E

Vf = CMftf

tf

E is said to be much more constant than

{mB) so unless the correction term is quite

small the equation containing E may be preferred. However, confidence in the accuracy of

results obtained with either equation is impaired if the correction is not small.

Some typical values for the various corrections used with our Cannon Master viscometers

are shown in table 5. These are intended only

to indicate the magnitude of the corrections

when the instruments are used with petroleum

Table 5. Approximate ranges of correction for

Cannon Master viscometers

Correction

Oil D Oil N

at 20 °C at 210 °F at 20 °C at 210 °F

0 to +0.018

0 —0.032

+0.144

0 to +0.018

—0.135

—0.009 +0.163

0 to +0.014

0 —0.015

+0.133

0 to +0.014

—0.078

+0.008 Xy +0.153

Total +0.112 to +0.130

+0.019 to +0.037

+0.118 to +0.132 +0.083 to +0.097

"Assume filling temperature between 20 and 30 °C (68-86 °F).

oils and the calibration constants are appropri- | ate for the conditions associated with opera- i tion at 20 °C with water. If the corrections for

the oil calibrated instruments were on the

basis of reference to calibration conditions ' with oil at 20 °C, the value of the Xy correction

would be reduced to not more than about 0.02 or 0.03 percent for liquids with values for y in ' the range 20 to 32 dynes/cm. However, it ' should not be overlooked that the percentage

corrections would be larger for instruments

[ having bulbs of about the same size but much ! lower values for h. For example, since the ^ bulb sizes are about the same for the Cannon , Master and the Cannon Fenske viscometers but ; the value of h for the Cannon Fenske instru- ) ments is only about 1/5 of that for the Cannon rf Master viscometers, the values of Xi, X„, and I] Xy for the smaller instruments are about five II times as great as for the Master viscometers. |i Not all the corrections discussed are neces- ? sary with all the types of instruments shown

^ in figure 1. The capillaries are essentially i straight, and bends are made only in tubes with i diameters considerably larger than the capillary and in which both the fluid velocity and re- sistance to flow are relatively low. Probably i no corrections for curvature, heating effect, or 1 drainage need be applied to these instruments

j when not used with externally applied pressure, i All of the instruments may require correction j for changes in the value of g if calibrated and |I used at different locations and all are subject [' to alinement error, air column correction, sur-

^ face tension effects, and thermal expansion of

j the instrument ; however, these corrections may |^ be negligibly small. For types (b), (c), (d),

j and (g) the correction for expansion of the i instrument is included in the correction for \ temperature of test. Instrument types (b), (c),

\ (d), and (g) may require a correction for the

^ temperature of filling as well as for the tem- i perature of test. The error resulting from mis-

^ alinement was discussed to point out the need '

for careful reproducible positioning of the in-

| strument. It is not anticipated that these

j| instruments would be used intentionally with j improper alinement, the error of alinement j measured, and a correction applied. The SIL \ and the Ubbelohde instruments are designed so

j that the capillary effects of the two liquid sur- | faces will in large measure neutralize each I other so that Xy for these instruments probably

j is negligible. Also, for these two instruments,

as well as for the straight-tube viscometer, the ! working volume of liquid is adjusted at each \ test temperature, eliminating the need for cor- i rections X-^ and X„. '

18
7. Calibration of Viscometers With a Reference Viscometer

The preceding discussion has been written

from the viewpoint that relative viscometers

will be calibrated with liquids whose viscosities are known explicitly at a specified temperature.

This is the usual practice in the United States,

although some prefer to calibrate relative capillary tube viscometers by direct comparison

with a calibrated viscometer of similar design

and range. This direct comparison method is

preferred in some countries where viscometer

calibrating liquids are not so readily available.

Briefly the method consists of determining

the flow times of one or more suitable liquids

in a calibrated viscometer and in the viscometer

to be calibrated. The determinations are made

by the same method that would be used if the

purpose were to determine the viscosity of the

liquid, except that there is no concern that the

measurements be made at a specific temperature—only that both instruments be at the

same temperature and that the determinations

be made concurrently. Then if eq (7) is applicable,

V = Cata = Chti

or (20)

Cft = Ca • u

The subscripts a and b refer, respectively, to

values associated with the reference instrument

and the instrument to be calibrated.

If the instrument is to be used in a range

where the end corrections are not negligible,

comparisons with two liquids will be required.

The two liquids should be chosen so that the

end correction for one will be substantial and

for the other negligible. If the end corrections

for one liquid are negligible in both instruments

the value of d, may be determined as just described using eq (20). Then (mB)i may be

evaluated by use of eq (21) and the flow times

for the other liquid. However, if the end cor- rections for neither of the liquids are negligible

for both viscometers, simultaneous equations

based on either eq (6) or eq (8) may be written and solved to determine the constants for

the instrument to be calibrated. For example,

using eq (6) we would write

_ (mB)a _ ^ ^ ^ {mB)b — ^af^ae — Ofttbe 5 tae tie

(21) _ {mB)a ^, (mB)i

Vf — UoCq/ — i^bHf • taf tif

(22)

The advantages cited for this procedure are

(a) that errors due to faulty temperature

measurement and control are avoided, since it

is not necessary to make the comparison at an

accurately known temperature and (b) that

since the glass capillary tube viscometers are much less subject to change with age than are

the calibrating liquids, they may be used as reference standards repeatedly over a long

period of time.

Although the first point may be valid with

regard to the calibration of an instrument, it should not be construed as in any way suggesting the lack of need for accurate measurement

and control of temperature when the instrument is used for measuring the viscosity of a

liquid.

The superior stability of the instruments

may be utilized in both methods, since after an

instrument has been calibrated with a refer- ence liquid (or viscometer) it may be preserved

as a reference standard for the laboratory and

used to recalibrate the reference liquid or to

calibrate new reference liquids as required.

One serious limitation of the direct comparison method is that, in general, it may be

used only for instruments of the same or similar design and range. At least, it is not readily

apparent how direct comparisons may be

effected between capillary tube instruments and

various rotational viscometers, falling body viscometers, etc., or even between some glass capillary tube vicometers of different designs.

In using the direct comparison method, the

corrections appropriate for each instrument

should be applied. If the reference viscometer

was calibrated in a different laboratory, the

possible need for adjustment of the instrument

constant, Ca, for differences in the strength of

the earth's gravitational field should not be

overlooked. Also, special care should be used to

duplicate the instrument alinement and operating procedure used in the calibration of the

reference viscometer.

In comparing the merits of the two methods,

it should be recognized that the appropriate

value for the instrument constant is affected by

the temperature, place, and method of use as

well as by the design and dimensions of the

instrument, and certain properties (surface

tension and coefficient of thermal expansion)

of the liquid being examined. On the other

hand, the viscosity of a reference liquid is

affected by its temperature but not by its geographic location or the method by which it was

determined, and of course it is more subject to

change with age. This statement assumes that

Newtonian behavior is an essential characteristic of a reference liquid for viscometry and

that, if necessary, the viscosity value has been

corrected to the standard pressure of one atmosphere.

19
Ordinarily when external pressure is not applied, the pressure correction is neglected and

in most instances lacks significance. However,

when measurements of more than routine ac- curacy are desired, the correction for barometric pressure may be large enough to warrant consideration if the work is being done in a laboratory situated at a considerable elevation. For example, it is estimated that at Denver, Colo, (elevation 5374 ft, normal barometric

pressure 625 mm of Hg) correction of measured viscosity values to account for the effect

of ambient pressure less than 1 atm would

range from about +0.016 percent to +0.065

percent for petroleum oils with viscosities

ranging from 0.01 poise to 100 poises. Such

correction would be necessary to account for

the pressure sensitivity of the liquid. Changes ; in barometric pressure would not affect the

value of the instrument constant. ' These estimates are based on the empirical | relation

'

Ar,% = (3 + 0.91 log »,) 10-^ Ap, (23) '

I where Aiy is the change in viscosity, in poises,

, resulting from a pressure differing from one I atmosphere by Ap mm of Hg. Equation (23) : was derived from relationships proposed by

'

Cragoe [9], using 3 X 10"* mm Hg as a repre1

sentative value for the pressure coefficient of I viscosity of petroleum oils. j

8. Precalibrated Viscometers

Formerly the Bureau provided a viscometer

calibration service covering a few types of

capillary tube viscometers. This service was

discontinued January 1, 1958 because of the

relatively small demand and the belief that

calibrations performed in the laboratory where

the viscometers were to be used were to be

preferred because the effects of any peculiarities of operating technique and accessory

equipment may tend to cancel when they are

the same for both the calibration and the

measurements on unknown samples.

Since precalibrated viscometers, i.e., instruments which have been calibrated some place

other than where used, usually are calibrated

with petroleum oils at 100 °F, it may be well to

point out to those working with nonpetroleum

liquids that some adjustment of the calibration

constants may be desirable to account for differ- ences between the surface tension of petroleum

oils and the liquids to be measured, as well as for the difference between the temperatures of

calibration and use. Probably this will not be

necessary with instruments of types similar to

(e) and (f) of figure 1 since for these instruments the volume of charge is not critical and

the net effect of surface tension is small. As

noted above, some adjustment of the instrument

constant to compensate for differences in gravity may be necessary when an instrument is

used at different locations. The need for such

adjustment could be determined by the user of

the instrument if the calibration certificate

contains a statement as to the acceleration due

to gravity in the calibrating laboratory.

For the more common types of U-tube viscometers for which appreciable correction may

be required for thermal expansion of the liquid

and for surface tension effects, a correction factor" M may be determined as indicated above to

adjust for differences between conditions when

calibrated at 100 °F with petroleum liquid and

the hypothetical conditions of filling and calibrating with water at 20 °C. This would be the

same factor that would be used if the viscosity

of the calibrating oil were being determined in a water-calibrated instrument. Then

c = ^,

Mo

where the subscript o indicates the value as- sociated with the calibrating oil and C is the

constant applicable to the hypothetical use with

water at 20 °C. Using the subscript I to indicate

values associated with another liquid, we may

write

vj = Citi = CMiti;

Ml

Ci = CMi = Co

Mo

9. References

[1] N. E. Dorsey, Phys. 28, 833 (Oct. 1926).

[2] J. F. Swindells, J. R. Coe, Jr., and T. B. Godfrey,

J. Research NBS 48, 1 (1952) (RP2279).

[3] Supplement to NBS Circular 440.

[4] Roger S. Porter and Julian F. Johnson, Bulk and

solution flow properties of polybutenes, ACS

Division of Polymer Chem. 1, No. 1 (Apr.

1960).

20

[5] J. F. Swindells, R. C. Hardy, and R. L. Cottington, J. Research NBS 52, 105 (1954) (RP2479).

[6] ASTM D445 Test for Kinematic Viscosity, 1960

Supplement to Book of ASTM Standards, Pt 7.

Unless the properties of the calibrating oil are known, typicalj values for a and a- may be assumed to be 0.0007/°C and 0.068 cm^

respectively, and the value of M for a Cannon-Fenske viscometer may be expected to be about 1.006. I

i
[7] M. R. Cannon, R. E. Manning, and J. D. Bell, [9] S. Sugden, J. Chem. Soc. London 119, 1483 (1921).

Anal. Chem. 32, 355 (1960). [10] C. S. Cragoe, Proc. World Petrol. Congress, Lon-

[8] F. Bashforth and J. C. Adams, Capillary Action don, 1933, Vol. II, p. 529.

(University Press, Cambridge, 1883).

10. Symbols

a

B

b

C

cD

d

capillary constant =

E =

/

9

H

h

J

K =

I =

m = M =

n —

P =

P' =

QR

Re =

constant factor in kinetic energy cor- rection term.

radius of curvature of meniscus at its

center.

instrument constant applicable under

conditions associated with real or

hypothetical calibration with water

at 20 °C.

specific heat of liquid.

diameter of capillary tube,

horizontal distance between upper

and lower bulbs of a U-tube viscometer.

constant (approximately) factor in

kinetic energy correction term, proposed by Cannon et al. height of meniscus in fiducial bulb at

mean time above the lower fiducial

mark.

factor for adjusting viscometer dimensions for thermal expansion;

force.

variable ratio v/t.

acceleration due to gravity.

total pressure causing flow when ex- ternal pressure is used, expressed

as head of test liquid.

difference between the levels of the

two free liquid surfaces.

height of mid-point of zone above

lower fiducial mark of experimental

bulb.

constant of proportionality in Poiseuille's equation,

length of capillary tube; length,

length of a portion of capillary tube

where flow is not affected by end

conditions,

coefficient of the Hagenbach or kinetic energy correction; mass,

combined correction factor,

coefficient of the Couette correction to

length of the capillary tube,

pressure difference between ends of

capillary tube,

pressure drop through a length V of

tube remote from the ends,

volume rate of flow through capillary,

radius of receiving bulb or lower

meniscus.

vdp

Reynolds number = . V radius of capillary tube.

T =

t =

V =

V

X =

a =

y -=

e =

n —

6 =

change in level of liquid surface in

receiving bulb as the fiducial bulb

is emptied or filled.

temperature.

time for liquid to flow from or into

the fiducial bulb; time,

volume of liquid flowing from or into

the fiducial bulb,

volume of liquid charge in viscometer,

average velocity of liquid flowing in

capillary.

fractional change in effective value of

h due to various differences between conditions during calibration

and use. mean volume coefficient of thermal

expansion of the liquid.

mean volume coefficient of thermal

expansion of the instrument glass.

surface tension of the liquid.

difference between 1 atm and the

pressure on the liquid.

mean linear coefficient of thermal ex- pansion of the instrument glass.

viscosity.

angle between the axis of the viscometer and the line of action of

gravity.

Couette correction to length of capillary.

kinematic viscosity = .

p = density of liquid or air. ^ = angle between the axis of the fiducial

bulb and the normal to the bulb

profile at the point of tangency between the meniscus and the bulb

< 90° when normal is below

horizontal)

.

Subscript Indicates value associated with:

1 temperature at which viscometer is

filled; value of « for temperature

interval - Tc.

the second of two or more liquids,

reference viscometer,

zone boundary; viscometer to be calibrated by direct comparison,

lower or receiving bulb,

time or place of calibration,

any two calibrating liquids e and /.

fiducial bulb,

geometry of instrument.

2

a

b

B

cej

F

9

21
increment of liquid,

liquid under examination,

calibration with petroleum oil at 100

°F.

external pressure.

receiving bulb.

V at Tc after filling at T^.

tube used in experiment to determine!

hy.

j time or place of use; or unknown,

water. i zone; volume increment in bulb,

surface tension effect.

^ U.S. eOVERNMENT PRINTING OFFICE: 1963 647S69

22
U.S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

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