Page 30 - Bird R.B. Transport phenomena

§1.1 Newton's Law of Viscosity (Molecular Transport of Momentum) 15

Table 1.1-4 Viscosities of Some Liquid Metals

Temperature Viscosity
Metal T(°C) /x (mPa • s)

Li 183.4 0.5918
216.0 0.5406
285.5 0.4548
Na 103.7 0.686
250 0.381
700 0.182
К 69.6 0.515
250 0.258
700 0.136
Hg -20 1.85
20 1.55
100 1.21
200 1.01
Pb 441 2.116
551 1.700
844 1.185
Data taken from The Reactor Handbook, Vol. 2, Atomic
Energy Commission AECD-3646, U.S. Government
Printing Office, Washington, D.C. (May 1955), pp. 258
et seq.

given for pure fluids at 1 atm pressure. Note that for gases at low density, the viscosity
increases with increasing temperature, whereas for liquids the viscosity usually decreases
with increasing temperature. In gases the momentum is transported by the molecules in
free flight between collisions, but in liquids the transport takes place predominantly by
virtue of the intermolecular forces that pairs of molecules experience as they wind their
way around among their neighbors. In §§1.4 and 1.5 we give some elementary kinetic
theory arguments to explain the temperature dependence of viscosity.

2
EXAMPLE 1.1-1 Compute the steady-state momentum flux т in lty/ft when the lower plate velocity V in Fig.
ух
1.1-1 is 1 ft/s in the positive x direction, the plate separation У is 0.001 ft, and the fluid viscos-
Calculation of ity ix is 0.7 cp.
Momentum Flux
SOLUTION
Since т is desired in British units, we should convert the viscosity into that system of units.
ух
5
Thus, making use of Appendix F, we find /x = (0.7 cp)(2.0886 X 10" ) = 1.46 X 10~ lb, s/ft .
2
5
The velocity profile is linear so that
dv bv -1.0 ft/s
x = x = = -lOOOs" 1 (1.1-5)
dy Ду ~ 0.001 ft
Substitution into Eq. 1.1-2 gives
2
5
r = -fi^ = -(1.46 X 10~ )(-1000) = 1.46 X 10" lb/ft 2 (1.1-6)
yx
ay '