## Viscosity

### Definitions and Methods of Measurement

The viscosity of a fluid (liquid or gas) is that property which tends to resist a shearing force. Since motion or flow of a fluid is produced by shearing forces, viscosity is associated with fluid motion. There is no relation between the viscosity and the specific gravity of most liquids. For instance, molasses having the same specific gravity (1.48) and the same Brix rating (90) may vary in viscosity from 128,000 to 303,000 Seconds Saybolt Universal (SSU). In rotodynamic pumps, fluid viscosity can have a significant impact on performance. ANSI/HI 9.6.7 acts as a guideline that explains these effects.

There are two basic viscosity parameters: dynamic (or absolute) viscosity and kinematic viscosity. (See the Kinematic and Dynamic Viscosity Conversion Tool to perform viscosity conversions.) The dynamic viscosity may be defined with the aid of Fig. 1 which shows two parallel plane surfaces of area (A) separated a distance (d) and the space between completely filled with fluid. A force (F) is applied to and in the plane of the upper surface, causing it to move with a velocity (v) parallel to the lower fixed surface. The velocity distribution will be linear over the distance (d) and experiments show that the slope of the velocity line (v/d) will be directly proportional to the unit shearing force (τ = F/A) for all "true" or "Newtonian" fluids. The proportionality factor (μ) is the dynamic viscosity. The foregoing may be expressed by the equations

(2.C.1) $$τ = {F \over A} = μ{v \over d}$$

(2.C.2) $$μ = {τ \over {v/d}}$$

Therefore, the dimensions of the dynamic viscosity are

$$force{time \over {length^2}}$$

The kinematic viscosity (𝜈) may be obtained by dividing the dynamic viscosity (μ) by the mass density (ρ). The mass density is the specific weight (w) divided by the acceleration of gravity (g). These relationships may be expressed by the equation

(2.C.3) $$ν = {μ \over {w/g}} = {μ \over ρ}$$

Therefore, the dimensions of kinematic viscosity are

$${length^2} \over time$$

The distinction between the dynamic and the kinematic viscosity should be carefully noted so that the correct parameter will be used as required in computations. Some useful relationships are as follows:

1 pound = 444,823 dynes

1 foot = 30.4800 centimeters

1 square foot = 929.034 square centimeters

1 dyne-second per sq cm = 1 poise = 100 centipoise

1 sq cm/sec = 1 stoke = 100 centistokes

1 lb-sec/sq ft = 478.801 poises = 47,880.1 centipoise

μ lb-sec/sq ft = (μ/47,880.1)centipoise = 0.0000208855 centipoise

𝜈 sq ft/sec = 𝜈 sq cm/sec / 929.034 = 0.00107639 stokes

𝜈 = μ/ρ = μ/(w/g)

𝜈 sq ft/sec = 0.000671970(μ/w)

where:

• w =
• g =

The viscosities of most fluids vary appreciably with changes in temperature. The influence of change in pressure usually is negligible.

The viscosities of fluids, such as mineral oil and water, are unaffected by the magnitude and kind of motion to which they may be subjected as long as the temperature remains constant. Thus the ratio of shear stress to shear rate is a constant for all shear rates, is independent of time, and zero shear rate exists only at zero shear stress; such a fluid is said to be Newtonian.

When the ratio of shear stress to shear rate increases as the shear rate increases, reversibly and independent of time, a fluid is said to be dilatent.

When the shear stress to shear rate ratio is constant for shear rates above zero, is independent of time, but when shear occurs only for shear stress above a fixed minimum greater than zero, a fluid is said to be plastic.

When the ratio of shear stress to shear rate decreases as shear rate increases, reversibly and independent of time, and zero shear rate occurs only at zero shear stress, a fluid is said to be pseudo-plastic.

When the ratio of shear stress to shear rate decreases as shear rate increases and is time dependent in that this ratio increases back to its "rest" value gradually with lapse of time at zero shear rate and stress, and decreases to a limit value gradually with lapse of time at constant shear rate, a fluid is said to be thixotropic.

When the shear stress to shear ratio rate is constant for all shear rates at any given instant of time, but increases with time, a fluid is said to be rheopectic.

Viscosity is measured by an instrument called a viscosimeter. A definite volume of fluid is allowed to flow through a capillary tube or orifice of specified proportions and the time of efflux noted. Instruments of the capillary type, such as the Ostwald, Bingham, and Ubbelohde viscosimeters are used primarily for fluids of low viscosity, such as water. Instruments of the orifice type are used commercially for more viscous fluids such as petroleum products, and the time of efflux of the sample is taken as a measure of the viscosity. The Saybolt viscosimeter is commonly used in the United States, the Saybolt Universal for fluids of medium viscosity and the Saybolt Furol for those of high viscosity. The viscosity is expressed in Seconds Saybolt Universal (SSU) or Seconds Saybolt Furol (SSF). The relationship between Saybolt Universal viscosities and kinematic viscosities in centistokes is given in "ASTM Conversion Tables for Kinematic and Saybolt Universal Viscosities" or by the ASTM Standard, Designation: D446-85a*. Similar information for Saybolt Furol viscosities may be obtained from the ASTM Standard, Designation: D2161-87. The respective British counterparts of the Saybolt Universal and Saybolt Furol viscosimeters are the Redwood and Redwood Admiralty viscosimeters. The Engler viscosimeter is used extensively on the continent of Europe. Viscosimeters such as the Brookfield are particularly useful with non-Newtonian fluids. There are many other viscosimeters for special purposes, discussion of which is beyond the scope of this Manual. Viscosity conversion tables for use with the above described viscosimeters are shown below. A viscosity blending chart for use with oils is also shown below. Let oil (A) have the higher viscosity and oil (B) the lower viscosity. Mark the viscosity of (A) and (B) on the right and left hand scales, respectively, and draw a straight line connecting the marks as shown. The viscosity of any blend of (A) and (B) will be shown by the intersection of the vertical line representing the percentage composition and the line described above.

*American Society for Testing Materials, 1916 Race St., Philadelphia. Pa. 19103.

### Viscosity Conversion Tables

The following tables will give an approximate comparison of various viscosity ratings so that if the viscosity is given in terms other than Saybolt Universal, it can be translated quickly by following horizontally to the Saybolt Universal column.

Conversions
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Seconds Saybolt Furol (SSF) Seconds Redwood (Standard) Seconds Redwood (Admirality) Degrees Engler Degrees Barbey Seconds Parlin Cup #7 Seconds Parlin Cup #10 Seconds Parlin Cup #15 Seconds Parlin Cup #20 Seconds Ford Cup #3 Seconds Ford Cup #4
31 1.00 29 1.00 6200
35 2.56 32.1 1.16 2420
40 4.30 36.2 5.10 1.31 1440
50 7.40 44.3 5.83 1.58 838
60 10.3 52.3 6.77 1.88 618
70 13.1 12.95 60.9 7.60 2.17 483
80 15.7 13.7 69.2 8.44 2.45 404
90 18.2 14.44 77.6 9.30 2.73 348
100 20.6 15.24 85.6 10.12 3.02 307
150 32.1 19.3 128 14.48 4.48 195
200 43.2 23.5 170 18.90 5.92 144 40
250 54.0 28 212 23.45 7.35 114 46
300 65.0 32.5 254 28 8.79 95 52.5 15 6.0 3 30 20
400 87.6 41.9 338 37.1 11.70 70.8 66 21 7.2 3.2 42 28
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Seconds Saybolt Furol (SSF) Seconds Redwood (Standard) Seconds Redwood (Admirality) Degrees Engler Degrees Barbey Seconds Parlin Cup #7 Seconds Parlin Cup #10 Seconds Parlin Cup #15 Seconds Parlin Cup #20 Seconds Ford Cup #3 Seconds Ford Cup #4
500 110 51.6 423 46.2 14.60 56.4 79 25 7.8 3.4 50 34
600 132 61.4 508 55.4 17.50 47 92 30 8.5 3.6 58 40
700 154 71.1 592 64.6 20.45 40.3 106 35 9.0 3.9 67 45
800 176 81 677 73.8 23.35 35.2 120 39 9.8 4.1 74 50
900 198 91 762 83 26.30 31.3 135 41 10.7 4.3 82 57
1000 220 100.7 896 92.1 29.20 28.2 149 43 11.5 4.5 90 62
1500 330 150 1270 138.2 43.80 18.7 65 15.2 6.3 132 90
2000 440 200 1690 184.2 58.40 14.1 86 19.5 7.5 172 118
2500 550 250 2120 230 73.00 11.3 108 24.0 9 218 147
3000 660 300 2540 276 87.60 9.4 129 28.5 11 258 172
4000 880 400 3380 368 117 7.05 172 37 14 337 230
5000 1100 500 4230 461 146 5.64 215 47 18 425 290
6000 1320 600 5080 553 175 4.70 258 57 22 520 350
7000 1540 700 5920 645 205 4.03 300 67 25 600 410
8000 1760 800 6770 737 234 3.52 344 76 29 680 465
9000 1980 900 7620 829 263 3.13 387 86 32 780 520
10000 2200 1000 8460 921 292 2.82 430 96 35 850 575
15000 3300 1500 13700 438 2.50 650 147 53 1280 860
20000 4400 2000 18400 584 1.40 860 203 70 1715 1150
Conversions
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Seconds Saybolt Furol (SSF) Seconds Redwood (Standard) Seconds Redwood (Admirality) Degrees Engler Degrees Barbey Seconds Parlin Cup #7 Seconds Parlin Cup #10 Seconds Parlin Cup #15 Seconds Parlin Cup #20 Seconds Ford Cup #3 Seconds Ford Cup #4
31 1.00 29 1.00 6200
35 2.56 32.1 1.16 2420
40 4.30 36.2 5.10 1.31 1440
50 7.40 44.3 5.83 1.58 838
60 10.3 52.3 6.77 1.88 618
70 13.1 12.95 60.9 7.60 2.17 483
80 15.7 13.7 69.2 8.44 2.45 404
90 18.2 14.44 77.6 9.30 2.73 348
100 20.6 15.24 85.6 10.12 3.02 307
150 32.1 19.3 128 14.48 4.48 195
200 43.2 23.5 170 18.90 5.92 144 40
250 54.0 28 212 23.45 7.35 114 46
300 65.0 32.5 254 28 8.79 95 52.5 15 6.0 3 30 20
400 87.6 41.9 338 37.1 11.70 70.8 66 21 7.2 3.2 42 28
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Seconds Saybolt Furol (SSF) Seconds Redwood (Standard) Seconds Redwood (Admirality) Degrees Engler Degrees Barbey Seconds Parlin Cup #7 Seconds Parlin Cup #10 Seconds Parlin Cup #15 Seconds Parlin Cup #20 Seconds Ford Cup #3 Seconds Ford Cup #4
500 110 51.6 423 46.2 14.60 56.4 79 25 7.8 3.4 50 34
600 132 61.4 508 55.4 17.50 47 92 30 8.5 3.6 58 40
700 154 71.1 592 64.6 20.45 40.3 106 35 9.0 3.9 67 45
800 176 81 677 73.8 23.35 35.2 120 39 9.8 4.1 74 50
900 198 91 762 83 26.30 31.3 135 41 10.7 4.3 82 57
1000 220 100.7 896 92.1 29.20 28.2 149 43 11.5 4.5 90 62
1500 330 150 1270 138.2 43.80 18.7 65 15.2 6.3 132 90
2000 440 200 1690 184.2 58.40 14.1 86 19.5 7.5 172 118
2500 550 250 2120 230 73.00 11.3 108 24.0 9 218 147
3000 660 300 2540 276 87.60 9.4 129 28.5 11 258 172
4000 880 400 3380 368 117 7.05 172 37 14 337 230
5000 1100 500 4230 461 146 5.64 215 47 18 425 290
6000 1320 600 5080 553 175 4.70 258 57 22 520 350
7000 1540 700 5920 645 205 4.03 300 67 25 600 410
8000 1760 800 6770 737 234 3.52 344 76 29 680 465
9000 1980 900 7620 829 263 3.13 387 86 32 780 520
10000 2200 1000 8460 921 292 2.82 430 96 35 850 575
15000 3300 1500 13700 438 2.50 650 147 53 1280 860
20000 4400 2000 18400 584 1.40 860 203 70 1715 1150

Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Approx. Seconds Mac Michael Approx. Gardner Holt Bubble Seconds Zahn Cup #1 Seconds Zahn Cup #2 Seconds Zahn Cup #3 Seconds Zahn Cup #4 Seconds Zahn Cup #5 Seconds Demmler Cup #1 Seconds Demmler Cup #10 Approx. Seconds Stormer (100 gm load) Seconds Pratt and Lambert "F"
31 1.00
35 2.56
40 4.30 1.3
50 7.40 2.3 2.6
60 10.3 3.2 3.6
70 13.1 4.1 4.6
80 15.7 4.9 5.5
90 18.2 5.7 6.4
100 20.6 125 38 18 6.5 7.3
150 32.1 145 47 20 10.0 1.0 11.3
200 43.2 165 A 54 23 13.5 1.4 15.2
250 54 198 A 62 26 16.9 1.7 19
300 65 225 B 73 29 20.4 2.0 23
400 87.6 270 C 90 37 27.4 2.7 31 7
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Approx. Seconds Mac Michael Approx. Gardner Holt Bubble Seconds Zahn Cup #1 Seconds Zahn Cup #2 Seconds Zahn Cup #3 Seconds Zahn Cup #4 Seconds Zahn Cup #5 Seconds Demmler Cup #1 Seconds Demmler Cup #10 Approx. Seconds Stormer (100 gm load) Seconds Pratt and Lambert "F"
500 110 320 D 46 34.5 3.5 39 8
600 132 370 F 55 41 4.1 46 9
700 154 420 G 63 22.5 48 4.8 54 9.5
800 176 470 72 24.5 55 5.5 62 10.8
900 198 515 H 80 27 18 62 6.2 70 11.9
1000 220 570 I 88 29 20 13 69 6.9 77 12.4
1500 330 805 M 40 28 18 103 10.3 116 16.8
2000 440 1070 Q 51 34 24 137 13.7 154 22
2500 550 1325 T 63 41 29 172 17.2 193 27.6
3000 660 1690 U 75 48 33 206 20.6 232 33.7
4000 880 2110 V 63 43 275 27.5 308 45
5000 1100 2635 W 77 50 344 34.4 385 55.8
6000 1320 3145 X 65 413 41.3 462 65.5
7000 1540 3670 75 481 48 540 77
8000 1760 4170 Y 86 550 55 618 89
9000 1980 4700 96 620 62 695 102
10000 2200 5220 Z 690 69 770 113
15000 3300 7720 Z2 1030 103 1160 172
20000 4400 10500 Z3 1370 137 1540 234
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Approx. Seconds Mac Michael Approx. Gardner Holt Bubble Seconds Zahn Cup #1 Seconds Zahn Cup #2 Seconds Zahn Cup #3 Seconds Zahn Cup #4 Seconds Zahn Cup #5 Seconds Demmler Cup #1 Seconds Demmler Cup #10 Approx. Seconds Stormer (100 gm load) Seconds Pratt and Lambert "F"
31 1.00
35 2.56
40 4.30 1.3
50 7.40 2.3 2.6
60 10.3 3.2 3.6
70 13.1 4.1 4.6
80 15.7 4.9 5.5
90 18.2 5.7 6.4
100 20.6 125 38 18 6.5 7.3
150 32.1 145 47 20 10.0 1.0 11.3
200 43.2 165 A 54 23 13.5 1.4 15.2
250 54 198 A 62 26 16.9 1.7 19
300 65 225 B 73 29 20.4 2.0 23
400 87.6 270 C 90 37 27.4 2.7 31 7
Seconds Saybolt Universal (SSU) Kinematic Viscosity Centistokes* Approx. Seconds Mac Michael Approx. Gardner Holt Bubble Seconds Zahn Cup #1 Seconds Zahn Cup #2 Seconds Zahn Cup #3 Seconds Zahn Cup #4 Seconds Zahn Cup #5 Seconds Demmler Cup #1 Seconds Demmler Cup #10 Approx. Seconds Stormer (100 gm load) Seconds Pratt and Lambert "F"
500 110 320 D 46 34.5 3.5 39 8
600 132 370 F 55 41 4.1 46 9
700 154 420 G 63 22.5 48 4.8 54 9.5
800 176 470 72 24.5 55 5.5 62 10.8
900 198 515 H 80 27 18 62 6.2 70 11.9
1000 220 570 I 88 29 20 13 69 6.9 77 12.4
1500 330 805 M 40 28 18 103 10.3 116 16.8
2000 440 1070 Q 51 34 24 137 13.7 154 22
2500 550 1325 T 63 41 29 172 17.2 193 27.6
3000 660 1690 U 75 48 33 206 20.6 232 33.7
4000 880 2110 V 63 43 275 27.5 308 45
5000 1100 2635 W 77 50 344 34.4 385 55.8
6000 1320 3145 X 65 413 41.3 462 65.5
7000 1540 3670 75 481 48 540 77
8000 1760 4170 Y 86 550 55 618 89
9000 1980 4700 96 620 62 695 102
10000 2200 5220 Z 690 69 770 113
15000 3300 7720 Z2 1030 103 1160 172
20000 4400 10500 Z3 1370 137 1540 234

* $$Kinematic\,Viscosity\,(in\,centistokes) = {{Absolute\,Viscosity\,(in\,centipoise)} \over Density\,(in\,g/cm^3)}$$

When the Metric System terms centistokes and centipoise are used, the density is numerically equal to the specific gravity. Therefore, the following expression can be used which will be sufficiently accurate for most calculations:

$$Kinematic\,Viscosity\,(in\,centistokes) = {{Absolute\,Viscosity\,(in\,centipoise)} \over Specific\,Gravity}$$

When the English System units are used, the density must be used rather than the specific gravity.

For values of 70 centistokes and above, use the following conversion:

$$SSU = centistokes * 4.635$$

Above the range of this table and within the range of the viscosimeter, multiply the particular value by the following approximate factors to convert to SSU:

Conversion Factors
Viscosimeter Factor
Saybolt Furol 10
Redwood Standard 1.095
Engler-Degrees 34.5
Parlin cup #15 98.2
Parlin cup #20 187
Ford cup #4 17.4
Mac Michael 1.92 (approx.)
Demmler #1 14.6
Demmler #10 146
Stormer 13 (approx.)
Conversion Factors
Viscosimeter Factor
Saybolt Furol 10
Redwood Standard 1.095
Engler-Degrees 34.5
Parlin cup #15 98.2
Parlin cup #20 187
Ford cup #4 17.4
Mac Michael 1.92 (approx.)
Demmler #1 14.6
Demmler #10 146
Stormer 13 (approx.)

### References

1. Hydraulic Institute, Engineering Data Book, Second Edition, 1990, Figure IIC-2.

Last updated on May 12th, 2020