36 www.cepmagazine.org October 2002 C E P

Measurement and Control

he flow characteristics of a flowmeter are usual-ly expressed as the flow of standard fluids, suchas air and water at the standard conditions oftemperature (T0 = 21.1°C; 70°F) and pressure

(1 atm). The flowmeter manufacturer normally suppliesthese data together with methods of converting them to theflow of any other fluid over a suitable range of conditionswhere the density and viscosity are known. This informationfor many fluids is given in tabular or graphical form. Thecorrelations presented in this article express the viscosity ofliquids in analytical form as a function of temperature.

The Othmer plot displays the log of a function (in thiscase, that which describes viscosity of a liquid), against thelog of the vapor pressure of water at the same temperature,which results in a straight line for practically all com-pounds. This can be expressed in graphical form as anomograph. In order to obtain an analytical expression, itis necessary to express the vapor pressure of water as ananalytical equation. This article uses the Antoine equationfor this purpose.

The viscosity of gases is independent of pressure untilthe pressure exceeds 10 atm. Above this value, the viscosityof the gas is correlated by another Othmer plot, namely thelog of the viscosity vs. log Pk/ρ, where Pk = P + a/V2; Pk =kinetic pressure of gas, P = gas pressure, a = van der Waalsconstant, V = molar volume and ρ = density of the gas.

This article provides a method of correlating the viscos-ity of liquids using the same type of Othmer plot used forgases. Since for flowmeter calculations the viscosity of liq-uids can be taken as independent of pressure, there is noneed to correlate liquid viscosity vs. pressure.

The liquid viscosity correlation is based on the samelinear equation as that for the viscosity of gases:

log µ = M log pw + N (1)

where µ is the liquid viscosity, pw is vapor pressure ofwater, M is slope and N is the y-intercept if a graph of log µvs. log pw were to be plotted. From this correlation, thenomograph in Figure 1 was constructed (1, 2).

For gases and liquids, the viscosity scale is logarith-mic, while the temperature scale is nonlinear and isbased upon its relationship to the log of the vapor pres-sure of the reference substance. This is shown graphical-ly in Figure 1.

The x and y coordinates for various liquids that areneeded to use Figure 1 are listed in Tables 1a and 1b.To obtain the viscosity, µ, of a particular liquid in cen-tipoise, at a liquid temperature of T, first plot the point(x, y) for the liquid on the grid. Then, draw a straightline from that point through the temperature on theleft-hand y-axis. Extend the line to the right, so that itintersects with the right-hand y-axis, which gives theviscosity. Note that for all flowmeter calculations, theviscosity of the liquid may be taken as independent ofpressure.

Analytical solutionTo obtain an analytical solution to Eq. 1, the value of

pw, which is a function of temperature, must be trans-formed into an analytical function. The Antoine equationfor vapor pressure was selected because it has a desirableaccuracy with a minimum number of parameters. The An-toine equation is stated as:

log pw = –D/(T + F) + E (2)

For water, the parameters D, E and F have the followingvalues: D = 1,722, E = 8.052 and F = 233 (3). The vaporpressure of the water, pw, is measured in torr at a tempera-ture (T) measured in °C.

Combining Eqs. 1 and 2, then making some simplifyingsubstitutions, one obtains the final working equation:

log µ = G/(T + F) + H (3)

where G = –MD and H = ME + N. Eq. 3 can also be usedto obtain µ0 at T0 = 21.1°C (standard temperature):

log µ0 = G/(T0+ F) + H (4)

TRoger Gilmont, Gilmont and Associates

Liquid Viscosity Correlationsfor Flowmeter Calculations

Use these graphs and equations to calculateliquid viscosity at any temperature.

C E P October 2002 www.cepmagazine.org 37

Combining Eq. 3 and 4, one obtains:

Let Z = 1/ (T + F) – 1/(T0 + F) (6)

and combine with Eq. 5 to yield:log µ = log µ0 + GZ (7)

Substituting the values: F = 233 and T0 = 21.1 into Eq. 5yields:

The same substitution of F and T0 intoEq. 6 yields:

Z = 1/(T + F) – 0.003935 (9)

Using Eq. 7, one obtains a plot oflog µ vs. Z for a given compound (suchas those listed in Tables 1a and 1b).This plot is a straight line with a slopeof G and a y-intercept of log µ0. Eq. 7can be used to determine µ at any de-sired temperature, for any compound.Subsequently, the analytically derivedvalue of µ at a given temperature can becompared with the value of µ obtainedby using Figure 1.

Let’s look at a sample calculation foracetaldehyde. From Table 1a, x = 15.2and y = 4.8. When this point is plottedon Figure 1, we see that at standard tem-perature (T0 = 21.1°C), µ0 = 0.223. At T= 100°C, Figure 1 reveals that µ =0.128. Z is calculated from Eq. 9: Z =[(1/(100 + 233) – 0.003935] = –0.000932. G is calculated by rearrang-ing Eq. 7: G = [log(µ/µ0)]/Z = [log(0.128/0.223)]/(–0.000932) = 258.7.This is the value of G that appears inTable 2 for acetaldehyde.

This value of G, which is constant,can be used to calculate µ via Eq. 7 at agiven temperature. This value of µ willbe compared to that obtained from Fig-ure 1 to determine the nomograph’s ac-curacy. Let us find µ at 50°C.

At 50°C, Z is calculated from Eq. 9to be –0.0004014. From Eq. 7, log µ =log µ0 + GZ = –0.6517 +(258.7)(–0.0004014) = –0.7555, and µ =

0.176. From Figure 1, µ at 50°C = 0.18.The average difference between the calculated values of µ

and those obtained from the nomograph is about 1%. Themaximum difference ranges from 3 to 5%, with the highererror found at the higher values of µ. Not all of the com-pounds listed in Tables 1a and 1b are included in Tables 2aand 2b — those compounds that are not liquids at normalconditions are omitted.

Viscosity of glycerol Glycerol’s viscosity is extremely sensitive to the amount

of water present in it. This makes it difficult to measure theviscosity of glycerol directly. In this article, glycerol pre-sents a challenge because its viscosity cannot be deter-mined by using the nomograph when the temperature isbelow 60°C. (Figure 1 limits the measurable viscosity of

log log µ µ= ++

−

( )01233

1254 1

8GT .

log log +

µ µ= + −+

( )0

0

1 1 5GT F T F

■ Figure 1. Nomograph of viscosity vs. temperature for liquids listed in Tables 1a and 1b. To use,plot the fluid’s (x, y) coordinates, and on the left-hand y-axis, plot the temperature. Draw a straight linethrough these points to the right-hand y-axis to obtain the viscosity.

200

190

180

380

360

340

320

300

280

260

240

220

200

180

160

140

120

100

80

60

40

20

-20

0

170

160

150

140

130

120

110

10030

28

26

24

22

20

18

16

14

12

10

8

6

4

2

00

Source: (2).

2 4 6 8 10

x

Tem

pera

ture

, ˚C

Tem

pera

ture

, ˚F

Visc

osity

, cP

y

12 14 16 18 20

90

80

70

60

50

40

30

-30

20

-20

10

-10

0

100

80

6050

40

30

20

10

8

65

4

3

2

1

0.8

0.60.5

0.4

0.3

0.2

0.1

glycerol to 100 cP, which occurs at approximately 60°C).In order to obtain the viscosity of glycerol at temperaturesbelow 60°C, Figure 1 must be extrapolated, and the newcorrelation, Eq. 7, must be used.

Table 3 lists values of Z over the temperature range T= 0°C to T = 100°C calculated using Eq. 9. It also givesthe viscosities for glycerol from 0°C to 30°C, whichwere obtained from Ref. 4, and the logarithms of thesevalues.

A plot of the log µ vs. Z based on this table is shown inFigure 2. The slope of this line is calculated as G =(y2–y1)/(x2–x1) between T = 0°C and T = 30°C, where: y2 =4.195 (at T = 0°C) and y1 = 2.870 (at T = 30°C); x2 = Z (at0°C) = 0.0003563 and x1 = Z (at 30°C) = –0.0001332. Thus,G = [(4.195–2.870)/(0.0005)] = 2,650. The intercept of thisgraph, Z0 at T0 = 21.1°C, is log µ0 = 3.135. Now, Eq. 7 canbe used to calculate viscosity of glycerol at any temperature.

Let’s calculate µ at 25°C and com-pare it with the value of µ found in the lit-erature. The log µc = 3.135 +2,650(–0.0000595) = 2.9773, so log µc =949. The error, ε, is calculated as ε =100[(µc–µ)/µc] = 100[(949–954)/949] =–0.5%. A similar calculation at T = 50°Cyields log µc = 3.135 + 2,650(–0.0004019)= 2.070, so µc = 117.5.

A comparison of the data points from the literature withthe correlated ones appears in Table 3. For the range of0–30°C, the average deviation (using the sum of the abso-lute values of ε) is 2.2%. If the data points at 15°C and

38 www.cepmagazine.org October 2002 C E P

Liquid X Y Liquid X YAcetaldehyde 15.2 4.8 m-Cresol 2.5 20.8Acetic acid, 100% 12.1 14.2 Cyclohexane 9.8 12.9Acetic acid, 70% 9.5 17.0 Cyclohexanol 2.9 24.3Acetic anhydride 12.7 12.8 Dibromoethane 12.7 15.8Acetone, 100% 14.5 7.2 Dichloroethane 13.2 12.2Acetone, 35% 7.9 15.0 Dichloromethane 14.6 8.9Acetonitrile 14.4 7.4 Diethyl ketone 13.5 9.2Acrylic acid 12.3 13.9 Diethyl oxalate 11.0 16.4Allyl alcohol 10.2 14.3 Diethylene glycol 5.0 24.7Allyl bromide 14.4 9.6 Dimethyl oxalate 12.3 15.8Allyl Iodide 14.0 11.7 Diphenyl 12.0 18.3Ammonia, 100% 12.6 2.0 Dipropyl ether 13.2 8.6Ammonia, 26% 10.6 13.9 Dipropyl oxalate 10.3 17.7Amyl acetate 11.8 12.5 Ethyl acetate 13.7 9.1Amyl alcohol 7.5 18.4 Ethyl acrylate 12.7 10.4Aniline 8.1 18.7 Ethyl alcohol, 100% 10.5 13.8Anisole 12.3 13.5 Ethyl alcohol, 95% 9.8 14.3Arsenic trichloride 13.9 14.5 Ethyl alcohol, 40% 6.5 16.6Benzene 12.5 10.9 Ethyl benzene 13.2 11.5Brine, CaCl2, 25% 6.6 15.9 Ethyl bromide 14.5 8.1Brine, NaCl, 25% 10.2 16.6 2-Ethyl butyl acrylate 11.2 14.0Bromine 14.2 13.2 Ethyl chloride 14.8 6.0Bromotoluene 20.0 15.9 Ethyl ether 14.5 5.3Butyl acetate 12.3 11.0 Ethyl formate 14.2 8.4i-Butyl acetate 13.1 11.3 Ethyl iodide 14.7 10.3n-Butyl acrylate 11.5 12.6 Ethyl propionate 13.2 9.9Butyl alcohol 8.6 17.2 Ethyl propyl ether 14.0 7.0i-Butyl bromide 13.1 10.9 Ethyl sulfide 13.8 8.9i-Butyl chloride 13.1 9.1 Ethylene bromide 11.9 15.7i-Butyl iodide 13.3 12.4 Ethylene chloride 12.7 12.2Butyric acid 12.1 15.3 Ethylene glycol 6.0 23.6Carbon dioxide 11.6 0.3 2-Ethyl hexyl acrylate 9.0 15.0Carbon disulfide 16.1 7.5 Ethylidene chloride 13.6 9.5Carbon tetrachloride 12.7 13.1 Fluorobenzene 13.7 10.4Chlorobenzene 12.3 12.4 Formic acid 10.7 15.8Chloroform 14.4 10.2 Freon-11 14.4 9.0Chlorosulfonic acid 11.2 18.1 Freon-12 16.8 5.6o-Chlorotoluene 13.0 13.3 Freon-21 15.7 7.5m-Chlorotoluene 13.3 12.5 Freon-22 17.2 4.7p-Chlorotoluene 13.3 12.5 Freon-113 12.5 11.4Source: (2).

Table 1a. x and y values for liquid viscosity nomograph (Figure 1).

Measurement and Control

NomenclatureD = constant in Antoine equation E = constant in Antoine equation F = constant in Antoine equation G = –MD (Eq. 7)G0 = value of G at T0H = constant defined as ME + N using Antoine

constants D, E and F (Eq. 3)M = slope of log µ vs. log pw plot N = intercept of log µ vs. log pw plotP = pressure at which a gas’s viscosity

becomes dependent upon pressure (greater than 10 atm)

Pk = kinematic pressure of gas used in an Othmer plot to determine the gas’s viscosity at pressures greater than 10 atm

pw = vapor pressure of water, torrT = temperature, °CTo = standard temperature = 21.1°CX = Z × 104

Z = [1/(T + F) + 1/(T0 + F)]

Greek Symbolsε = [(µc – µ)/µc] × 100; percent error between

correlated (or calculated) value of µ obtainedfrom Figure 1 or from literature

µ = viscosity, cP µo = viscosity at T0 (21.1°C)µc = calculated viscosity for glycerol example

Further ReadingThis article is Part 4 of a series of articles that appeared in Measurement &

Control (M&C), which is now defunct. Part 1 (M&C, Dec. 1998, p. 92)discussed finding the density of real gases for use in flowmeter calcula-tions. Part 2 (M&C, June 1999, p. 83) presented methods of correlatingthe density of liquids using an Othmer plot of the log of the density ofthe compound versus the log of the density of a reference substance.Part 3 (M&C, Oct. 1999, p. 78) showed gow to use the Othmer plot forcorrelating the viscosity of the gases vs. the log of the vapor pressure ofa reference substance at the same temperature. This article covers cor-relations for the viscosity of liquids using the same type of Othmer plotused for gases.

30°C, which vary somewhat from thestraight line, are omitted, the error isonly 0.9%. The coordinates in Table1b for glycerol should be corrected tox = 0 and y = 27.7 in order to obtaingood agreement at temperaturesabove 50°C. The correlated valuescan be expected to have an averageerror of 0.9% for the range of50–100°C.

Viscosity of water The viscosity of water does not fol-

low the correlation because the plot oflog µ vs. Z is not a straight line. Table4 lists the viscosity of water at20–100°C, from data in Ref. 4, and aplot of log µ vs. Z and G vs. Z isshown in Figure 3. The curvature ofthe plot indicates that G is not a con-stant. The values of G in Table 4 wereobtained implicitly for each value of µby rearranging Eq. 7 and solving forG. To render Eq. 7 an accurate correla-tion for water, G will be treated as aquadratic function of Z:

G'= G0 + AX + BX2 (10)

where X = Z × 104. To find G0 at21.1°C, one must interpolate betweenG at T = 20°C and T = 40°C; G0 =670.3.

Eq. 10 can be transformed into alinear equation as follows:

(G' – G0)/X = A + BX

Define Δ = (G' – G0)/X = A + BX (11)

The values of Δ can be calculated for water at the tem-peratures in Table 4. These values are plotted against X (orZ × 104) in Figure 3. Since this plot is lin-ear, we can find the values of the slope, B,and the y-intercept, A, by reading them di-rectly from the graph:At X = 0, A = Δ = 12.80, and B = (12.8 –9.81)/[(0 – (–10)] = 0.299.

We now have a quadratic expressionfor G that can be used in Eq. 10 to find µc:

G' = 670.3 + 12.8X + 0.299X2

= 670.3 + 12.8(Z × 104) + 0.299(Z2 × 108) (12)

log µc = log µ0 + G'(Z) (13)

If T = 20°C, then log µc = –0.0093 + (0.0000171) ×[670.3 + 12.8(0.171) + 0.299(0.0292)] = 0.0022, and µc= 1.0051.

C E P October 2002 www.cepmagazine.org 39

Liquid x y Liquid x yGlycerol, 100% 2.0 30.0 Phenol 6.9 20.8Glycerol, 50% 6.9 19.6 Phosphorous tribromide 13.8 16.7Heptene 14.1 8.4 Phosphorous trichloride 16.2 10.9Hexane 14.7 7.0 Propionic acid 12.8 13.8Hydrochloric acid, 31.5% 13.0 16.6 Propyl acetate 13.1 10.3Iodobenzene 12.8 15.9 Propyl alcohol 9.1 16.5Isobutyl alcohol 7.1 18.0 Propyl bromide 14.5 9.6Isobutyric acid 12.2 14.4 i- Propyl bromide 14.1 9.2Isopropyl alcohol 8.2 16.0 Propyl chloride 14.4 7.5Kerosene 10.2 16.9 i-Propyl chloride 13.9 7.1Linseed oil, raw 7.5 27.2 Propyl formate 13.1 9.7Mercury 18.4 16.4 Propylene glycol 3.1 23.7Methanol, 100% 12.4 10.5 Propyl iodide 14.1 11.6Methanol, 90% 12.3 11.8 i-Propyl iodide 13.7 11.2Methanol, 40% 7.8 15.5 Sodium 16.4 13.9Methyl acetate 14.2 8.2 Sodium hydroxide, 50% 3.2 25.8Methyl acrylate 13.0 9.5 Stannic chloride 13.5 12.8Methyl i-butyrate 12.3 9.7 Succinonitrile 10.1 20.8Methyl n-butyrate 13.2 10.3 Sulfur dioxide 15.2 7.1Methyl chloride 15.0 3.8 Sulfuric acid, 110% 7.2 27.4Methyl ethyl ketone 13.9 8.6 Sulfuric acid, 100% 8.0 25.1Methylene chloride 14.1 8.7 Sulfuric acid, 98% 7.0 24.8Methyl formate 14.2 7.5 Sulfuric acid, 60% 10.2 21.3Methyl iodide 14.3 9.3 Sulfuryl chloride 15.2 12.4Methyl propionate 13.5 9.0 Tetrachloroethane 11.9 15.7Methyl propyl ketone 14.3 9.5 Tetrachloroethylene 14.2 12.7Methyl sulfide 15.3 6.4 Thiophene 13.2 11.0Naphthalene 7.9 18.1 Titanium tetrachloride 14.4 12.3Nitric acid, 95% 12.8 13.8 Toluene 13.7 10.4Nitric acid, 60% 10.8 17.0 Trichloroethylene 14.8 10.5Nitrobenzene 10.6 16.2 Triethylene glycol 4.7 24.8Nitrogen dioxide 12.9 8.6 Turpentine 11.5 14.9Nitrotoluene 11.0 17.0 Vinyl acetate 14.0 8.8Octane 13.7 10.0 Vinyl toluene 13.4 12.0Octyl alcohol 6.6 21.1 Water 10.2 13.0Pentachloroethane 10.9 17.3 o-Xylene 13.5 12.1Pentane 14.9 5.2 m-Xylene 13.9 10.6 p-Xylene 13.9 10.9Source: (2).

Table 1b. x and y values for liquid viscosity nomograph (Figure 1).

Table 3. Glycerol viscosity vs. temperature.T °C Z µ† log µ µc ε

0 0.0003563 12,100 4.083 12,000 –0.96 0.0002486 6,260 3.797 6,220 –0.615 0.0000968 2,330 3.367 2,463 +5.420 0.0000171 1,490 3.173 1,515 +1.725 –0.0000595 954 2.980 949 –0.530 –0.0001332 629 2.799 605 –4.050 –0.0004019 No Data 117.5 –100 –0.0009325 No Data 4.63 –†Source: (4).

40 www.cepmagazine.org October 2002 C E P

Table 2b. Constants for compounds from Figure 1 for use with Eq. 7.

Compound µ0 log µ0 G Compound µ0 log µ0 GGlycerol 1365 3.135 2650 Propionic acid 1.12 0.0492 404.6Heptene 0.42 –0.3768 331.9 Propyl acetate 0.57 –0.2441 393.5Hexane 0.331 –0.4801 330.2 n-Propyl alcohol 2.32 0.3655 734.2Iodobenzene 1.11 0.2330 416.2 Propyl bromide 0.51 –0.2924 300.6Isobutyl alcohol 4.05 0.6075 984.2 i-Propyl bromide 0.482 –0.3170 328.8Isobutyric acid 1.30 0.1139 454.6 Propyl chloride 0.357 –0.4473 306.4Isopropyl alcohol 2.25 0.3522 854.0 i-Propyl chloride 0.321 –0.4935 339.3Methanol 0.59 –0.2291 449.3 Propyl formate 0.52 –0.2840 325.5Methyl acetate 0.408 –0.3893 327.6 Propylene glycol 50.1 1.6998 1658.4Methyl acrylate 0.50 –0.3010 404.3 Propyl iodide 0.62 –0.2076 329.5Methyl i-butyrate 0.50 –0.3010 446.0 i-Propyl iodide 0.70 –0.1549 349.3Methyl n-butyrate 0.59 –0.2291 381.9 Stannic chloride 0.91 –0.0410 353.6Methyl ethyl ketone 0.43 –0.3665 354.4 Succinonitrile 5.6 0.7482 627.6Methylene chloride 0.435 –0.3615 328.4 Sulfuric acid 22.0 1.3424 853.8Methyl formate 0.352 –0.4535 326.7 Sulfuryl chloride 0.87 –0.0605 266.6Methyl iodide 0.500 –0.3010 304.7 Tetrachloroethane 1.70 0.2304 483.7Methyl propionate 0.458 –0.3391 370.1 Tetrachloroethylene 1.72 0.2355 481.5Methyl propyl ketone 0.501 –0.3001 304.0 Thiophene 0.66 –0.1805 390.0Methyl sulfide 301 –0.5214 255.4 Titanium tetrachloride 0.85 –0.0706 311.1Nitric acid, 95% 1.13 0.0531 418.8 Toluene 0.60 –0.2218 362.4Nitrobenzene 2.05 0.3118 596.5 Trichloroethylene 0.61 –0.2146 285.5Nitrotoluene 3.35 0.3711 557.8 Triethylene glycol 42.5 1.6284 1340.1Octane 0.55 –0.2596 354.6 Vinyl acetate 0.450 –0.3468 336.6n-Octyl alcohol 10.0 1.0000 1028.5 Vinyl toluene 0.80 –0.0960 364.5Pentachloroethane 2.53 0.4031 566.6 Water 0.9788 –0.009 G(X)*Pentane 0.238 –0.6234 281.8 o-Xylene 0.83 –0.0809 369.1Phenol 8.5 0.9294 997.2 m-Xylene 0.61 –0.2147 343.8Phosphorous tribromide 1.90 0.2788 348.2. p-Xylene 0.65 –0.1871 329.1Phosphorous trichloride 0.66 –0.1805 199.6Source (3). *G’ = G 0 + AX + BX 2, where X = Z(104) and G 0 = 670.3, A = 12.80, B = 0.299 (for T = 20–100°C).

Measurement and Control

Table 2a. Constants for compounds from Figure 1 for use with Eq. 7.

Compound µ0 log µ0 G Compound µ0 log µ0 GAcetaldehyde 0.223 –0.6517 258.7 m-Chlorotoluene 0.88 –0.0555 381.6Acetic acid 1.28 0.1072 476.8 p-Chlorotoluene 0.88 –0.0555 381.6Acetic anhydride 0.91 –0.0410 419.3 m-Cresol 21.0 1.3222 1807Acetone 0.332 0.4789 306.4 Cyclohexane 1.0 0 646.0Acetonitrile 0.350 –0.4559 320.4 Cyclohexanol 70.0 1.8451 1719Acrylic acid 1.18 0.0719 449.2 Diethyl ketone 0.485 –0.3143 343.6Allyl alcohol 1.37 0.1367 635.8 Diethyl oxalate 2.11 0.3243 567.0Ally bromide 52 –0.2840 310.6 Diethylene glycol 39.0 1.5911 1303Allyl iodide 0.75 –0.1249 342.1 Dipropyl ether 0.423 –0.3737 400.7n-Amyl acetate 0.9 –0.0458 496.6 Dipropyl oxalate 2.80 0.4472 623.3n-Amyl alcohol 4.38 0.6415 911.1Aniline 4.35 0.6385 858.0 Ethyl acetate 0.475 –0.3233 360.8Anisole 1.10 0.0414 448.7 Ethyl acrylate 0.60 –0.2218 427.0Arsenic trichloride 1.30 0.1139 352.6 Ethyl alcohol 1.19 0.0755 596.2Benzene 0.65 –0.1871 436.1 Ethyl benzene 0.725 –0.1397 388.4Bromine 1.00 0 323.0 Ethyl bromide 0.400 –0.3979 300.3n-Butyl acetate 0.67 –0.1739 450.2 2-Ethyl butyl acrylate 1.25 0.0969 542.7i-Butyl acetate 0.72 –0.1427 404.8 Ethyl ether 0.237 –0.6253 294.3n-Butyl acrylate 0.90 –0.0458 511.9 Ethyl formate 0.425 –0.3716 328.5n-Butyl alcohol 2.9 0.4623 800.8 Ethyl iodide 0.600 –0.2218 293.0i-Butyl bromide 0.65 –0.1871 409.4 Ethyl propionate 0.53 –0.2757 344.6i-Butyl chloride 0.47 –0.3279 398.1 Ethyl propyl ether 0.320 –0.4949 337.7i-Butyl iodide 0.87 –0.0605 377.5 Ethyl sulfide 0.450 –0.3468 352.8Butyric acid 1.60 0.2041 472.8 Ethylene bromide 1.71 0.2330 480.3Carbon disulfide 0.37 0.4318 211.5 Ethylene chloride 0.85 –0.0706 429.7Carbon tetrachloride 1.00 0 427.0 Ethylene glycol 21.8 1.3385 1130Chlorobenzene 0.89 –0.0506 448.4 2-Ethyl hexyl acrylate 1.68 0.2253 754.2Chloroform 0.58 –0.2366 307.2 Ethylidene chloride 0.50 –0.3010 364.0Chlorosulfonic acid 3.00 0.4771 555.9 Fluorobenzene 0.60 –0.2218 350.2o-Chlorotoluene 1.07 0.0294 403.6 Formic acid 1.81 0.2577 581.2Source: (3).

The percent error between this value and that obtainedfrom literature is calculated as ε = (1.0051–1.0050)/1.0051 × 100 = +0.01%. The average error be-tween the data points and the correlated values in the range20–100°C is only ±0.026%. Since the data in this regionare only accurate to ±0.03%, the correlated values may beconsidered as valid as the tabulated ones.

Working exampleThis example illustrates the calculation of the viscosity

of hexane at 25°C. From Table 2b, log µ0 = –0.4801 and G= 330.2. From Eq. 9, Z = [1/(25 + 233) – 0.003935] =–5.903 × 10–5. Using Eq. 7, log µ = –0.4801 +(330.2)(–5.903 × 10–5) = –0.4996, and µ = 0.316, comparedwith 0.32 from Figure 1. C E P

C E P October 2002 www.cepmagazine.org 41

Table 4. Water viscosity vs. temperature.T °C Z µ† log µ G X X2 Δ µc ε20 0.0000171 1.0050 0.0022 672.5 0.171 0.0292 12.87 1.0051 +0.0121.1 0 0.9788 –0.0093 670.3 0 0 12.80 0.9788 —40 –0.0002725 0.6560 –0.1831 637.8 –2.725 7.426 11.93 0.6560 0.0060 –0.0005225 0.4688 –0.3290 611.9 –5.225 27.301 11.18 0.4689 +0.0280 –0.0007406 0.3565 –0.4479 592.2 –7.406 54.85 10.55 0.3566 +0.03100 –0.0009325 0.2838 –0.5470 576.6 –9.325 86.96 10.05 0.2836 –0.07†Source: (4).

■ Figure 2. Graph of log µ vs. Z (from Eq. 7) for glycerol. Values of µ arefrom Ref. 4.

4

3.5

3

2.5

0

051015202530

-2 -1 1

T˚C

2 3 4

Z × 104

log

µ

ROGER GILMONT is the retired president of Roger Gilmont Associates (38-41240th St., Douglaston, NY 11363; Phone/Fax: (718) 224-8711), exclusiveconsultants to Gilmont Instruments, a div of Barnant Co. Gilmont is a Fellowof the Polytechnic Univ. (Brooklyn, NY), where he was an adjunct professorin chemical engineering for 45 years, teaching thermodynamics andelectrochemical technology at the graduate and undergraduate levels. Heauthored a textbook on thermodynamic principles for chemical engineers,and has written more than 50 articles on thermodynamics, fluid flow andlaboratory instruments. He has also received over 30 patents in these areas.Gilmont is a member of the American Chemical Society and AIChE.

Literature Cited1. Othmer, D. F., and R. Gilmont, “Correlating Physical and Thermo-

dynamic Properties,” Petroleum Refiner, pp. 111–118 (Nov. 1951).2. Aronson, M. H., and R. C. Nelson, “Viscosity Measurement and

Control,” Instruments Publishing Co., Pittsburgh (1964).3. Gilmont, R., “Correlations for the Density and Viscosity of Fluids

for Flowmeter Calculations: Part 3, Viscosity of Gases,” Measure-ment and Control, pp. 78–83 (Oct. 1999).

4. Weats, R. C., “Handbook of Chemistry and Physics,” 53rd ed.,Chemical Rubber Publishing Co., Cleveland, OH (1972).

■ Figure 3. Graph of log µ, G and Δ vs. X (or Z × 104) for water. Values ofµ are from Ref. 4. Values of G are calculated using Eq. 7. Values of Δ arecalculated using Eq. 11.

0

-0.1

-0.2

-0.3

-0.4

-0.5

0.1

13

12 650

600

11

10

9

0.2

0

2060 4080100

-10 -5

X = Z × 104

log

µ

Log µ

G

T˚C

Δ

Δ

G