Viscosities 2.2.3



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

« Previous Subsection

Next Subsection »

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

mPa s

Temp.

°C

mPa s

Temp.

°C

mPa s

Temp.

°C

mPa s

1.792

1.0020

0.5471

0.3150

1.519

0.8902

0.4670

100

0.2821

1.307

0.7973

0.4046

125

0.2217

1.138

0.6526

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 = η_p/η₀ at same temperature.

Liquid	Temp./°C	Pressure/MPa
Liquid	Temp./°C	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