Viscousity Unit Engineering

There are two related measures of fluid viscosity - known as dynamic (or absolute) and kinematic viscosity.

Dynamic (absolute) Viscosity is the tangential force per unit area required to move one horizontal plane with respect to the other at unit velocity when maintained a unit distance apart by the fluid. The shearing stress between the layers of non turbulent fluid moving in straight parallel lines can be defined for a Newtonian fluid as:

The dynamic or absolute viscosity can be expressed like τ = μ dc/dy

(1)

where τ = shearing stress μ = dynamic viscosity Equation (1) is known as the Newtons Law of Friction. 2

In the SI system the dynamic viscosity units are N s/m , Pa s or kg/m s where 

1 Pa s = 1 N s/m2 = 1 kg/m s

The dynamic viscosity is also often expressed in the metric CGS (centimeter-gram-second) 2 system as g/cm.s, dyne.s/cm or poise (p) where 

1 poise = dyne s/cm2 = g/cm s = 1/10 Pa s

For practical use the Poise is to large and it's usual divided by 100 into the smaller unit called the centiPoise (cP) where 

1 p = 100 cP

o

o

Water at 68.4 F (20.2 C) has an absolute viscosity of one - 1 - centiPoise.

1 N s/m2 = 1 Pa s = 10 poise = 1,000 milliPa s

Kinematic Viscosity is the ratio of absolute or dynamic viscosity to density - a quantity in which no force is involved. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with it's mass density ν=μ/ρ

(2)

where ν = kinematic viscosity μ = absolute or dynamic viscosity ρ = density 2

In the SI-system the theoretical unit is m /s or commonly used Stoke (St) where 

1 St = 10-4 m2/s

Since the Stoke is an unpractical large unit, it is usual divided by 100 to give the unit called Centistokes (cSt) where  



1 St = 100 cSt 1 cSt = 10-6 m2/s 2 4 2 1 m /s = 1 x 10 cm /s =1 x 104 stokes = 1 x 106 centistokes o

o

Since the specific gravity of water at 68.4 F (20.2 C) is almost one (1), the kinematic viscosity of o water at 68.4 F is for all practical purposes 1.0 cSt.

Viscosity and Reference Temperatures The viscosity of a fluid is highly temperature dependent and for either dynamic or kinematic viscosity to be meaningful, the reference temperature must be quoted. In ISO 8217 the o reference temperature for a residual fluid is 100 C. For a distillate fluid the reference temperature o is 40 C.  

For a liquid - the kinematic viscosity will decrease with higher temperature For a gas - the kinematic viscosity will increase with higher temperature

Other Commonly used Viscosity Units

Saybolt Universal Seconds (or SUS, SSU) Saybolt Universal Seconds (or SUS) is used to measure viscosity. The efflux time is Saybolt Universal Seconds (SUS) required for 60 milliliters of a petroleum product to flow through the calibrated orifice of a Saybolt Universal viscometer, under carefully controlled temperature and as prescribed by test method ASTM D 88. This method has largely been replaced by the kinematic viscosity method. Saybolt Universal Seconds is also called the SSU number (Seconds Saybolt Universal) or SSF number (Saybolt Seconds Furol). Kinematic viscosity versus dynamic or absolute viscosity can be expressed as ν = 4.63 μ / SG

(3)

where ν = kinematic vicosity (SSU) μ = dynamic or absolute viscosity (cP)

Degree Engler Degree Engler is used in Great Britain as a scale to measure kinematic viscosity. Unlike the Saybolt and Redwood scales, the Engler scale is based on comparing a flow of the substance being tested to the flow of another substance - water. Viscosity in Engler degrees is the ratio of the time of a flow of 200 cubic centimetres of the fluid whose viscosity is being measured - to the o time of flow of 200 cubic centimeters of water at the same temperature (usually 20 C but o o sometimes 50 C or 100 C) in a standardized Engler viscosity meter.

Newtonian Fluids Fluids for which the shearing stress is linearly related to the rate of shearing strain are designated as Newtonian Fluids. Newtonian materials are referred to as true liquids since their viscosity or consistency is not affected by shear such as agitation or pumping at a constant temperature. Fortunately most common fluids, both liquids and gases, are Newtonian. Water and oils are examples of Newtonian liquids.

Shear-thinning or Pseudoplastic Liquids Shear-thinning or pseudoplastic liquids are those whose apparent viscosity decreases with increasing shear rate. Their structure is time-independent.

Thixotropic Fluids Thixotropic liquids have a time-dependent structure. The apparent viscosity of a thixotropic liquid decreases with increasing time, at a constant shear rate. Ketchup and mayonnaise are examples of thixotropic materials. They appear thick or viscous but are possible to pump quite easily.

Dilatant Fluids Shear Thickening Fluids or Dilatant Fluids increase their viscosity with agitation. Some of these liquids can become almost solid within a pump or pipe line. With agitation, cream becomes butter and Candy compounds, clay slurries and similar heavily filled liquids do the same thing.

Bingham Plastic Fluids Bingham Plastic Fluids have a yield value which must be exceeded before it will start to flow like a fluid. From that point the viscosity will decrease with increase of agitation. Toothpaste, mayonnaise and tomato catsup are examples of such products.

Example - Converting between Kinematic and Absolute Viscosity for Air 5

2

o

-6

2

Kinematic viscosity of air at 1 bar (10 Pa, N/m ) and 40 C is 16.97 cSt (16.97 10 m /s). The density of air estimated with the Ideal Gas Law ρ =p/RT where 3

ρ = density (kg/m ) 2

p = absolute pressure (Pa, N/m ) R = individual gas constant (J/kg K) T = absolute temperature (K) 5

2

o

0

ρ = (10 N/m ) / ((287 J/kg/K) (273 C + 33 C) = 1.113 kg/m

3

Absolute viscosity can be expressed as 3

-6

2

μ = (1.113 kg/m ) (16.97 10 m /s) -5

2

= 1.88 10 (kg/m s, Ns/m , P)

Viscosity and Specific Gravity of some Common Liquids Liquid

Temperature

o

( F)

o

( C)

Kinematic Viscosity Seconds CentiStokes Saybolt (cSt) Universal (SSU)

Acetaldehyde CH3CHO

61 68

16.1 20

0.305 0.295

36

Acetic acid - vinegar - 10% CH3COOH

59

15

1.35

31.7

Acetic acid - 50%

59

15

2.27

33

Acetic acid - 80%

59

15

2.85

35

Acetic acid - concentrated glacial

59

15

1.34

31.7

Acetic acid anhydride (CH3COO)2O

59

15

0.88

Acetone CH3COCH3

68

20

0.41

Alcohol - allyl

68 104

20 40

1.60 0.90 cp

31.8

Alcohol - butyl-n

68

20

3.64

38

Alcohol - ethyl (grain) C2H5OH

68 100

20 37.8

1.52 1.2

31.7 31.5

Alcohol - methyl (wood) CH3OH

59 32

15 0

0.74 1.04

Alcohol - propyl

68 122

20 50

2.8 1.4

35 31.7

Aluminum sulfate - 36% solution

68

20

1.41

31.7

Ammonia

0

-17.8

0.30

Aniline

68

20

4.37

40

50

10

6.4

46.4

Asphalt RC-0, MC-0, SC-0

77 100

25 37.8

159-324 60-108

737-1.5M 280-500

Automatic crankcase oil SAE 10W

0

-17.8

1295-max

6M-max

Automatic crankcase oil SAE 10W

0

-17.8

1295-2590 6M-12M

Automatic crankcase oil SAE 20W

0

-17.8

2590-10350 12M-48M

Automatic crankcase oil SAE 20

210

98.9

5.7-9.6

45-58

Automatic crankcase oil SAE 30

210

98.9

9.6-12.9

58-70

Automatic crankcase oil SAE 40

210

98.9

12.9-16.8

70-85

Automatic crankcase oil SAE 50

210

98.9

16.8-22.7

85-110

Automotive gear oil SAE 75W

210

98.9

4.2 min

40 min

Automotive gear oil SAE 80W

210

98.9

7.0 min

49 min

Automotive gear oil SAE 85W

210

98.9

11.0 min

63 min

Automotive gear oil SAE 90W

210

98.9

14-25

74-120

Automotive gear oil SAE 140

210

98.9

25-43

120-200

Automotive gear oil SAE150

210

98.9

43 - min

200 min

Beer

68

20

1.8

32

Benzene (Benzol) C6H6

32 68

0 20

1.0 0.74

31

Bone oil

130 212

54.4 100

47.5 11.6

220 65

Bromine

68

20

0.34

Butane-n

-50 30

-1.1

0.52 0.35

Butyric acid n

68 32

20 0

1.61 2.3 cp

Calcium chloride 5%

65

18.3

1.156

Calcium chloride 25%

60

15.6

4.0

39

Carbolic acid (phenol)

65 194

18.3 90

11.83 1.26 cp

65

Carbon tetrachloride CCl4

68 100

20 37.8

0.612 0.53

Carbon disulfide CS2

32 68

0 20

0.33 0.298

Castor oil

100 130

37.8 54.4

259-325 98-130

12001500 450-600

China wood oil

69 100

20.6 37.8

308.5 125.5

1425 580

31.6

Chloroform

68 140

20 60

0.38 0.35

Coconut oil

100 130

37.8 54.4

29.8-31.6 14.7-15.7

140-148 76-80

Cod oil (fish oil)

100 130

37.8 54.4

32.1 19.4

150 95

Corn oil

130 212

54.4 100

28.7 8.6

135 54

Corn starch solution, 22 Baumé

70 100

21.1 37.8

32.1 27.5

150 130

Corn starch solution, 24 Baumé

70 100

21.1 37.8

129.8 95.2

600 440

Corn starch solution, 25 Baumé

70 100

21.1 37.8

303 173.2

1400 800

Cotton seed oil

100 130

37.8 54.4

37.9 20.6

176 100

Crude oil 48o API

60 130

15.6 54.4

3.8 1.6

39 31.8

Crude oil 40o API

60 130

15.6 54.4

9.7 3.5

55.7 38

Crude oil 35.6o API

60 130

15.6 54.4

17.8 4.9

88.4 42.3

Crude oil 32.6o API

60 130

15.6 54.4

23.2 7.1

110 46.8

Decane-n

0 100

17.8 37.8

2.36 1.001

34 31

Diethyl glycol

70

21.1

32

149.7

Diethyl ether

68

20

0.32

Diesel fuel 2D

100 130

37.8 54.4

2-6 1.-3.97

32.6-45.5 -39

Diesel fuel 3D

100 130

37.8 54.4

6-11.75 3.97-6.78

45.5-65 39-48

Diesel fuel 4D

100 130

37.8 54.4

29.8 max 13.1 max

140 max 70 max

Diesel fuel 5D

122 160

50 71.1

86.6 max 35.2 max

400 max 165 max

Ethyl acetate CH3COOC2H3

59 68

15 20

0.4 0.49

Ethyl bromide C2H5Br

68

20

0.27

Ethylene bromide

68

20

0.787

Ethylene chloride

68

20

0.668

Ethylene glycol

70

21.1

17.8

88.4

Formic acid 10%

68

20

1.04

31

Formic acid 50%

68

20

1.2

31.5

Formic acid 80%

68

20

1.4

31.7

Formic acid concentrated

68 77

20 25

1.48 1.57cp

31.7

Freon -11

70

21.1

0.21

Freon -12

70

21.1

0.27

Freon -21

70

21.1

1.45

Furfurol

68 77

20 25

1.45 1.49cp

31.7

Fuel oil 1

70 100

21.1 37.8

2.39-4.28 -2.69

34-40 32-35

Fuel oil 2

70 100

21.1 37.8

3.0-7.4 2.11-4.28

36-50 33-40

Fuel oil 3

70 100

21.1 37.8

2.69-5.84 2.06-3.97

35-45 32.8-39

Fuel oil 5A

70 100

21.1 37.8

7.4-26.4 4.91-13.7

50-125 42-72

Fuel oil 5B

70 100

21.1 37.8

26.413.6-67.1

12572-310

Fuel oil 6

122 160

50 71.1

97.4-660 37.5-172

450-3M 175-780

Gas oils

70 100

21.1 37.8

13.9 7.4

73 50

Gasoline a

60 100

15.6 37.8

0.88 0.71

Gasoline b

60 100

15.6 37.8

0.64

Gasoline c

60 100

15.6 37.8

0.46 0.40

Glycerin 100%

68.6 100

20.3 37.8

648 176

2950 813

Glycerin 50% water

68 140

20 60

5.29 1.85 cp

43

Glucose

100 150

37.8 65.6

7.7M-22M 880-2420

35M100M 4M-11M

Heptanes-n

0 100

-17.8 37.8

0.928 0.511

Hexane-n

0 100

-17.8 37.8

0.683 0.401

Honey

100

37.8

73.6

349

Ink, printers

100 130

37.8 54.4

550-2200 238-660

250010M 1100-3M

Insulating oil

70 100

21.1 37.8

24.1 max 115 max 11.75 max 65 max

Kerosene

68

20

2.71

35

Jet Fuel

-30.

-34.4

7.9

52

Lard

100 130

37.8 54.4

62.1 34.3

287 160

Lard oil

100 130

37.8 54.4

41-47.5 23.4-27.1

190-220 112-128

Linseed oil

100 130

37.8 54.4

30.5 18.94

143 93

Mercury

70 100

21.1 37.8

0.118 0.11

Methyl acetate

68

20

0.44

104

40

0.32 cp

Methyl iodide

68 104

20 40

0.213 0.42 cp

Menhaden oil

100 130

37.8 54.4

29.8 18.2

140 90

Milk

68

20

1.13

31.5

Molasses A, first

100 130

37.8 54.4

281-5070 151-1760

130023500 700-8160

B, second

100 130

37.8 54.4

1410-13.2M 660-3.3M

653561180 305815294

12190255M 2630-55M 1320-16.5M 612076.5M

C, blackstrap

100 130

37.8 54.4

Naphthalene

176 212

80 100

0.9 0.78 cp

Neatstool oil

100 130

37.8 54.4

49.7 27.5

230 130

Nitrobenzene

68

20

1.67

31.8

Nonane-n

0 100

-17.8 37.8

1.728 0.807

32

Octane-n

0 100

-17.8 37.8

1.266 0.645

31.7

Olive oil

100 130

37.8 54.4

43.2 24.1

200

Palms oil

100 130

37.8 54.4

47.8 26.4

Peanut oil

100 130

37.8 54.4

42 23.4

Pentane-n

0 80

17.8 26.7

0.508 0.342

Petrolatum

130 160

54.4 71.1

20.5 15

100 77

Petroleum ether

60

15.6

31(est)

1.1

Propionic acid

32 68

0 20

1.52 cp 1.13

31.5

Propylene glycol

70

21.1

52

241

100-120

20.5-25

Quenching oil (typical)

200

Rapeseed oil

100 130

37.8 54.4

54.1 31

250 145

Rosin oil

100 130

37.8 54.4

324.7 129.9

1500 600

Rosin (wood)

100 200

37.8 93.3

Sesame seed oil

100 130

37.8 54.4

39.6 23

184 110

Sodium chloride 5%

68

20

1.097

31.1

Sodium chloride 25%

60

15.6

2.4

34

216-11M 1M-50M 108-4400 500-20M

Sodium hydroxide (caustic soda) 20%

65

18.3

4.0

39.4

Sodium hydroxide (caustic soda) 30%

65

18.3

10.0

58.1

Sodium hydroxide (caustic soda) 40%

65

18.3

Soya bean oil

100 130

37.8 54.4

35.4 19.64

165 96

Sperm oil

100 130

37.5 54.4

21-23 15.2

110 78

Sulphuric acid 100%

68 140

20 60

14.56 7.2 cp

76

Sulphuric acid 95%

68

20

14.5

75

Sulphuric acid 60%

68

20

4.4

41 3M-8M 650-1400

Sulphuric acid 20%

Tar, coke oven

70 100

21.1 37.8

600-1760 141-308

15M300M 2M-20M

Tar, gas house

70 100

21.1 37.8

3300-66M 440-4400

2500 500

Tar, pine

100 132

37.8 55.6

559 108.2

200-300 55-60

Toluene

68 140

20 60

0.68 0.38 cp

185.7

Triethylene glycol

70

21.1

40

400-440

185-205

Turpentine

100 130

37.8 54.4

86.5-95.2 39.9-44.3

Varnish, spar

68 100

20 37.8

313 143

Water, distilled

68

20

1.0038

31

Water, fresh

60 130

15.6 54.4

1.13 0.55

31.5

1.15

31.5 163-184 97-112

Water, sea

Whale oil

100 130

37.8 54.4

35-39.6 19.9-23.4

Xylene-o

68 104

20 40

0.93 0.623 cp

1425 650

centiStokes (cSt)

Saybolt Second Universal (SSU, SUS)

Typical liquid

1

31

Water (20oC)

4.3

40

Milk SAE 20 Crankcase Oil SAE 75 Gear Oil

15.7

80

No. 4 fuel oil

20.6

100

Cream

43.2

200

Vegetable oil

110

500

SAE 30 Crankcase Oil SAE 85 Gear Oil

220

1000

Tomato Juice SAE 50 Crankcase Oil SAE 90 Gear Oil

440

2000

SAE 140 Gear Oil

1100

5000

Glycerine (20oC) SAE 250 Gear Oil

2200

10,000

Honey

6250

28,000

Mayonnaise

19,000

86,000

Sour cream

Centipoise (CPS) Millipascal seconds (mPas)

Poise (P)

1

0.01

1

0.01

31

2

0.02

2

0.02

34

4

0.04

4

0.04

38

7

0.07

7

0.07

47

10

0.1

10

0.1

60

15

0.15

15

0.15

80

20

0.2

20

0.2

100

25

0.24

25

0.24

130

Saybolt Centistokes Stokes Seconds (cSt) (S) Universal (SSU)

30

0.3

30

0.3

160

40

0.4

40

0.4

210

50

0.5

50

0.5

260

60

0.6

60

0.6

320

70

0.7

70

0.7

370

80

0.8

80

0.8

430

90

0.9

90

0.9

480

100

1

100

1

530

120

1.2

120

1.2

580

140

1.4

140

1.4

690

160

1.6

160

1.6

790

180

1.8

180

1.8

900

200

2

200

2

1000

220

2.2

220

2.2

1100

240

2.4

240

2.4

1200

260

2.6

260

2.6

1280

280

2.8

280

2.8

1380

300

3

300

3

1475

320

3.2

320

3.2

1530

340

3.4

340

3.4

1630

360

3.6

360

3.6

1730

380

3.8

380

3.8

1850

400

4

400

4

1950

420

4.2

420

4.2

2050

440

4.4

440

4.4

2160

460

4.6

460

4.6

2270

480

4.8

480

4.8

2380

500

5

500

5

2480

550

5.5

550

5.5

2660

600

6

600

6

2900

700

7

700

7

3380

800

8

800

8

3880

900

9

900

9

4300

1000

10

1000

10

4600

1100

11

1100

11

5200

1200

12

1200

12

5620

1300

13

1300

13

6100

1400

14

1400

14

6480

1500

15

1500

15

7000

1600

16

1600

16

7500

1700

17

1700

17

8000

1800

18

1800

18

8500

1900

19

1900

19

9000

2000

20

2000

20

9400

2100

21

2100

21

9850

2200

22

2200

22

10300

2300

23

2300

23

10750

2400

24

2400

24

11200

2500

25

2500

25

11600

3000

30

3000

30

14500

3500

35

3500

35

16500

4000

40

4000

40

18500

4500

45

4500

45

21000

5000

50

5000

50

23500

5500

55

5500

55

26000

6000

60

6000

60

28000

6500

65

6500

65

30000

7000

70

7000

70

32500

7500

75

7500

75

35000

8000

80

8000

80

37000

8500

85

8500

85

39500

9000

90

9000

90

41080

9500

95

9500

95

43000

15000

150

15000

150

69400

20000

200

20000

200

92500

30000

300

30000

300

138500

40000

400

40000

400

185000

50000

500

50000

500

231000

60000

600

60000

600

277500

70000

700

70000

700

323500

80000

800

80000

800

370000

90000

900

90000

900

415500

100000

1000

100000

1000

462000

125000

1250

125000

1250

578000

150000

1500

150000

1500

694000

175000

1750

175000

1750

810000

200000

2000

200000

2000

925000

Kinematic viscosity can be converted from SSU to Centistokes like νCentistokes = 0.226 νSSU - 195 / νSSU where νSSU < 100 νCentistokes = 0.220 νSSU - 135 / νSSU where νSSU > 100

Viscosity and Temperature Kinematic viscosity of liquids like water, mercury, oils SAE 10 and oil no. 3 - and gases like air, hydrogen and helium are indicated below. Note that  

for liquids viscosity decreases with temperature for gases viscosity increases with temperature