spacer spacer Go to Kaye and Laby Home spacer
spacer
spacer spacer spacer
spacer
spacer
spacer
spacer spacer

You are here:

spacer

Chapter: 2 General physics
    Section: 2.2 Mechanical properties of materials
        SubSection: 2.2.3 Viscosities

spacer
spacer

spacer

« Previous Subsection

Next Subsection »

Unless otherwise stated this page contains Version 1.0 content (Read more about versions)

2.2.3 Viscosities

Viscosities of liquids

The dynamic viscosity, η of a (Newtonian) fluid is given by η = τ ÷ dv/dr; τ = shearing stress between two planes parallel with the direction of flow, dv/dr = velocity gradient at right angles to the direction of flow. The dimensions of dynamic viscosity are ML−1T−1, and the SI unit is Pa s.

Kinematic viscosity, ν, is the ratio of the dynamic viscosity to the density, ρ. The dimensions of kinematic viscosity are L2T−1 and the SI unit is m2 s−1.

Fluidity, is the reciprocal of the dynamic viscosity, η. The dynamic viscosity of liquids decreases with the temperature approximately according to the equation log η = A + B/T, where A and B are characteristic constants and T is the absolute temperature. Values of A and B for a large number of liquids are given by Barrer (1943).

(i) Viscosity of water. Data from Kestin, Sokolov and Wakeham (1978).


Temp.

°C

η

mPa s

Temp.

°C

η

mPa s

Temp.

°C

η

mPa s

Temp.

°C

η

mPa s

 

 

 

 

 

 

 

 

0

1.792

20

1.0020

50

0.5471

90

0.3150

5

1.519

25

0.8902

60

0.4670

100  

0.2821

10  

1.307

30

0.7973

70

0.4046

125  

0.2217

15  

1.138

40

0.6526

80

0.3551

150  

0.1818

 

 

 

 

 

 

 

 




(ii) Viscosities of various liquids. η in mPa s


Liquid

−100 °C

− 50 °C

0 °C

25 °C

30 °C

50 °C

75 °C

100 °C

 

 

 

 

 

 

 

 

 

Acetic acid    .    .

1.116

1.037

0.792

0.591

0.457

Acetone        .    .

0.402

0.310

0.295

0.247

0.200

0.165

Aniline          .    .

9.450

3.822

3.298

1.982

1.201

0.808

Benzene         .    .

0.603

0.562

0.436

0.332

0.263

Bromobenzene    .

1.592

1.065

0.995

0.780

0.605

0.488

n-Butane   .    .    .

0.747

0.339

0.197

0.157

0.150

Carbon disulphide

2.132

0.796

0.445

0.357

0.343

Carbon dioxide   .

0.227

0.098

0.057

Carbon tetrachloride

1.341

0.912

0.851

0.662

0.503

0.395

Chloroform    .    .

1.514

0.709

0.536

0.510

0.422

0.341

0.281

Di-ethyl ether     .

1.545

0.544

0.288

0.224

0.214

0.179

0.146

0.119

Ethanol    .    .    .

98.96    

8.318

1.873

1.084

0.983

0.684

0.459

0.323

Ethyl acetate      .

1.284

0.575

0.428

0.406

0.332

0.264

0.215

Ethyl formate     .

1.060

0.504

0.381

0.362

0.299

0.240

0.196

n-Hexane     .    .

0.782

0.387

0.296

0.282

0.235

0.190

0.155

n-Hexadecane   .

3.044

2.729

1.852

1.245

0.896

Mercury       .    .

1.616

1.528

1.497

1.401

1.322

1.255

Methane        .    .

  0.0357

—    

—   

—   

—   

—   

Methanol       .    .

2.258

0.797

0.543

0.507

0.392

0.294

0.227

Nitrobenzene      .

1.842

1.688

1.244

0.915

0.710

n-Octane       .    .

1.837

0.719

0.516

0.486

0.390

0.306

0.247

Oil, castor     .    .

700          

451           

125           

42.0      

16.9      

Oil, olive  .    .    .

67.0     

54.0      

25.8      

9.4    

7.0    

n-Pentane     .    .

1.300

0.498

0.273

0.214

0.205

0.173

0.140

0.115

n-Propane     .    .

0.421

0.215

0.127

0.099

0.094

—   

—   

—   

Sulphuric acid     .

23.8      

20.1      

11.7      

6.6    

4.1    

Toluene    .    .    .

2.124

0.768

0.551

0.520

0.420

0.334

0.272

 

 

 

 

 

 

 

 

 

For more data see: ESDU (1966–83), Landolt-Börstein (1969).




(iii) Viscosity of aqueous glycerol solutions. Data from Segur and Oberstar (1951), corrected to value for water at 20 °C of 1.002 mPa s.

Density
20° kg/l

% weight
glycerol

η/Pa s

20°C

30°C

40°C

 

 

 

 

 

1.2611

100  

1.408

0.610

0.283

1.2588

99

1.146

0.498

0.234

1.2562

98

0.936

0.408

0.195

1.2534

97

0.763

0.339

0.165

1.2508

96

0.622

0.280

0.142

1.2482

95

0.521

0.236

0.121

1.2085

80

   0.059 9

   0.033 8

   0.020 7

1.1254

50

     0.005 98

     0.004 20

     0.003 09

1.0459

20

     0.001 75

     0.001 35

     0.001 07

1.0215

10

     0.001 31

     0.001 03

       0.000 823

 

 

 

 

 




(iv) Viscosity of aqueous sucrose solutions. Data from Bingham and Jackson (1918), corrected to a more recent value for the viscosity of water.

Relative density
20°/4 °C

% weight
sucrose

 

η/Pa s

15 °C

20 °C

25 °C

1.3790

75

4.039   

2.328    

1.405    

1.3472

70

0.746 9

0.481 6

0.321 6

1.3163

65

0.211 3

0.147 2 

0.105 4

1.2865

60

  0.079 49

  0.058 49

  0.040 03

1.2296

50

  0.019 53

  0.015 43

  0.012 40

1.1764

40

    0.007 463

    0.006 167

    0.005 164

1.1270

30

    0.003 757

    0.003 187

    0.002 735




(v) Relative viscosities of some aqueous solutions at 1 N concentration. For a complete list see International Critical Tables (1928) and Stokes and Mills (1965). (The latter covers 1929–63.)

Substance

Temp./°C

Relative viscosity

Substance

Temp./°C

Relative viscosity

Ammonia    .    .    .    .    .

25

1.02

  Potassium chloride    .    .

17.6

0.98

Ammonium chloride   .    .

   17.6

0.98

  Potassium iodide       .    .

17.6

0.91

Calcium chloride   .    .    .

20

1.31

  Sodium hydroxide     .    .

25  

1.24

Hydrochloric acid   .    .    .

15

1.07

  Sulphuric acid      .    .    .

25  

1.09




(vi) Viscosity of liquid metals and molten salts. η in mPa s

Liquid

100 °C

400 °C

600 °C

700 °C

800 °C

1100 °C

1200 °C

Aluminium    .    .    .    .    .    .

2.96  

2.66

Gold       .    .    .    .    .    .    .

5.13

4.64

Lead      .     .    .    .    .    .    .

2.32

1.55

1.37  

1.24

Potassium          .    .    .    .    .

0.458

  0.224

  0.172

0.155

  0.141

Sodium        .    .    .    .    .    .

0.680

  0.286

  0.215

0.192

  0.174

Tin     .    .    .    .    .    .    .    .

1.33

1.04

0.95  

   0.89   

0.78

0.77

Potassium chloride       .    .    .

   1.096 

Potassium nitrate     .    .    .    .

2.09

1.07

Sodium chloride     .    .    .    .

    1.500

Sodium nitrate        .   .    .    .

1.91

    816°C.

For more data on molten salts see G. J. Janz (1968). For liquid metal see Smithell (1983, p. 14.2).




Viscosities of glasses and minerals. log10(η/Pa s)

Material

900 °C

1000 °C

1100 °C

1200 °C

1300 °C

1400 °C

1600 °C

1800 °C

2000 °C

                   

Plate glass     .    .

4.00

3.03

2.41

  1.87  

1.46

1.07

Medium flint glass 

3.9  

2.8  

1.9  

1.4  

0.9  

0.7  

Silica        .    .    .

14.6

12.7   

11.8    

9.7  

8.2

4.7

3.4

Olivine          .    .

2.5 

1.5  

1.2  

Diorite          .    .

3.1 

2.3  

1.8  

Diopside      .    .

0.52

0.43

 

 

 

 

 

 

 

 

 

 




Viscosities of liquids at high pressures

(i) Relative viscosity of water

Pressure/MPa

2.2 °C

10 °C

20 °C

30 °C

50 °C

75 °C

100 °C

               

        0.1

1.000

1.000

1.000

1.000

1.000

1.000

1.000

  49

0.946

0.969

0.990

0.998

1.021

1.029

1.043

  98

0.926

0.957

0.990

1.008

1.046

1.063

1.085

196

0.940

0.982

1.023

1.053

1.104

1.137

1.170

294

0.993

1.037

1.081

1.116

1.174

1.217

1.256

392

1.072

1.185

1.163

1.195

1.253

1.302

1.349

588

1.296

1.330

1.367

1.386

1.439

1.492

1.546

784

1.629

1.642

1.664

1.708

1.757

981

1.950

1.936

1.948

1.986

 

 

 

 

 

 

 

 




(ii) Relative viscosities of various liquids. Ratio = ηp/η0 at same temperature.

Liquid

Temp./°C

Pressure/MPa

98

100

392

400

784

1177

               

Acetone    .    .    .    .

30

1.68

4.03

 9.70

 

75

1.65

3.55

 7.36

13.7

Benzene    .    .    .    .

30

2.22

 

50

2.06

 

75

2.07

2.00

 

100  

1.98

  7.40

Carbon disulphide    .

30

1.45

3.23

 6.92

15.5

 

75

1.50

3.14

 6.25

11.8

Di-ethyl ether      .    .

30

2.11

6.20

18.2  

46.8

 

75

1.87

5.28

12.8  

27.1

Ethanol     .    .    .    .

30

1.59

4.14

10.5  

24.5

 

75

1.64

4.28

 9.48

18.3

n-Hexane .    .    .    .

25

2.10

 

30

2.15

8.20

32.7 

 

75

2.33

2.21

7.91

  7.41

 24.8  

69.7

 

100  

2.26

  7.22

n-Hexadecane      .    .

50

2.89

 

75

2.69

 

100  

2.61

15.0  

Methanol   .    .    .    .

30

1.47

2.96

5.62

   9.95

 

75

1.46

2.74

4.77

   7.69

n-Octane   .    .    .    .

25

2.31

12.9  

 

30

2.12

12.3   

 

75

2.20

2.24

8.97

 9.19

35.7   

 

100  

2.25

 8.56

n-Pentane  .    .    .    .

30

2.07

7.03

22.9   

70.2

 

75

2.25

7.33

20.3   

48.1

Toluene     .    .    .    .

30

1.87

7.89

50.0   

 

75 

1.86

6.33

24.6   

109    

 

 

 

 

 

 

 

 




Data from Bridgman (1926), except at 100 and 400 MPa which comes from K. J. Young, PhD Thesis, University of Glasgow, Nov. 1980, and Dymond, Robertson and Isdale (1981).


Viscosities of gases and vapours

(i) Viscosities at normal pressure. Units: μPa s.

Gas

0 °C

20 °C

50 °C

100 °C

200 °C

300 °C

400 °C

500 °C

600 °C

 

 

 

 

 

 

 

 

 

 

Air   .    .    .    .    .

17.3

18.2

19.6

22.0

26.1

29.8

33.2

36.4

39.4

Ammonia   .    .    .

  9.2

  9.9

11.0

13.0

16.8

20.6

24.4

28.2

31.9

Argon   .    .    .    .

21.0

22.3

24.2

27.3

32.8

37.7

42.2

46.4

50.4

Benzene     .    .    .

  7.0

  7.5

  8.1

  9.4

12.0

Carbon dioxide    .

13.7

14.7

16.1

18.5

23.0

27.1

30.8

34.2

37.4

Carbon monoxide

16.6

17.4

18.8

21.0

25.2

29.0

32.5

35.6

38.6

Chlorine    .    .    .

12.3

13.2

14.5

16.9

21.0

25.0

Chloroform    .    .

  9.4

10.1

11.1

12.8

16.2

19.5

Ethylene    .    .    .

  9.7

10.3

11.2

12.8

15.4

17.9

Helium

18.7

19.6

21.0

23.2

27.3

31.2

34.8

38.4

41.8

Hydrogen  .    .    .

  8.4

  8.8

  9.4

10.4

12.1

13.7

15.3

16.9

18.4

Krypton    .    .    . 

23.4

25.0

27.4

31.2

38.0

44.2

49.9

55.2

60.2

Methane   .    .    .

10.3

11.0

11.9

13.5

16.3

18.8

21.1

23.3

25.3

Neon        .    .    .

29.8

31.3

33.6

37.0

43.2

48.9

54.3

59.4

64.4

Nitrogen   .    .    .

16.6

17.6

18.9

21.2

25.1

28.6

31.9

34.9

37.8

Nitrous oxide .    .

13.7

14.7

16.1

18.4

22.9

27.0

30.7

34.0

37.0

Oxygen    .    .    .

19.5

20.4

21.8

24.4

29.3

33.7

37.6

41.3

44.7

Steam      .    .    .

  9.2

  9.7

10.6

12.4

16.2

20.3

24.5

28.6

32.6

Sulphur dioxide  .

11.6

12.6

14.0

16.4

20.9

25.1

29.0

32.6

36.1

Xenon    .    .    .

21.2

22.8

25.1

28.8

35.7

42.0

47.9

53.4

58.6

 

 

 

 

 

 

 

 

 

 

For viscosity of gases μPa s is a convenient size of unit. From the kinetic theory the viscosity is expected to be independent of pressure and to vary as the square root of the absolute temperature. The first is true except at very low and at high pressures; the second requires correction. Dividing the kinetic theory expression by a correction factor which is a linear function of the reciprocal of the absolute temperature leads to Sutherland’s formula η = KT3/2/(T + C), where K and C are constants characteristic of the gas. For higher accuracy a polynomial can be used instead of a linear factor.




(ii) Viscosities of some gases at high pressure. η/μPa s (all at 300 K)

Gas

 

Pressure/MPa

2

5

10

20

30

Air    .    .    .    .    .    .

18.7

19.3

20.5

23.7

27.5

Argon    .    .    .    .    .

23.3

24.0

25.7

30.5

36.4

Helium   .    .    .    .    .

19.9

19.9

20.0

20.1

20.3

Hydrogen    .    .    .   .

    8.98

    9.01

    9.09

    9.31

    9.59

Methane     .    .    .    .

11.6

12.3

14.0

19.2

24.7

Nitrogen.    .    .    .    .

18.3

18.9

20.1

23.2

26.8

Oxygen      .    .    .    .

20.9

21.5

22.9

27.1

32.2




(iii) Viscosity of nitrogen at high pressure. η/μPa s.

Temperature/K

Pressure/MPa

5

10

20

30

50

200

14.6

17.6

26.4

34.9

48.9

250

16.7

18.5

23.1

28.4

38.8

300

18.9

20.1

23.2

26.8

34.4

350

20.9

21.9

24.2

26.9

32.7

400

22.9

23.7

25.5

27.6

32.3

500

26.5

27.1

28.4

29.9

33.2




References

Barrer (1943) Trans. Farad., 39, 48.
Bingham and Jackson (1918) National Bureau of Standards, Bulletin, 14, 59.
P. W. Bridgman (1926) Proc. Am. Acad. Arts Sci., 61, 57–99.
J. H. Dymond, J. Robertson and J. D. Isdale (1981) Int. J. Thermophysics, 2(2), 133–154; ibid., 2(3), 223–236.
Engineering Science Data (ESDU) Physical Data (1966–83) Chemical Engineering, vol. 3, Viscosity, London.
International Critical Tables (1928).
G. J. Janz (1968) NSRDS-NBS 15, report, Natl. Bur. Standards, Washington.
Kestin, Sokolov and Wakeham (1978) J. Phys. Chem. Ref. Data, 7(3), 941.
Landolt-Börnstein (1969) Vol. II, Properties of Matter in its Aggregated States, Part 5a, Viscosity and Diffusion, 6th edn, Springer-Verlag, Berlin.
Segur and Oberstar (1951) Ind. Eng. Chem., 43, 2117.
Smithell (1983) Metal Reference Book, 6th edn, Butterworth, London, p. 14.2.
R. H. Stokes and R. Mills (1965) Viscosity of Electrolytes and Related Properties, Pergamon Press, London.
K. J. Young (1980) PhD Thesis, University of Glasgow.

J.T.R.Watson

spacer


spacer
spacer
spacer spacer spacer

Home | About | Table of Contents | Advanced Search | Copyright | Feedback | Privacy | ^ Top of Page ^

spacer

This site is hosted and maintained by the National Physical Laboratory © 2017.

spacer