Page 52 - Bird R.B. Transport phenomena

Problems 37

Table 1.7-2 Summary of Notation for Momentum Fluxes
Symbol Meaning Reference
pw Convective momentum-flux tensor Table 1.7-1
т Viscous momentum-flux tensor" Table 1.2-1
TT = pb + т Molecular momentum-flux tensor'' Table 1.2-1
p
ф = IT + w Combined momentum-flux tensor Eq. 1.7-2
" For viscoelastic fluids (see Chapter 8), this should be called the viscoelastic
momentum-flux tensor or the viscoelastic stress tensor.
b
This may be referred to as the molecular stress tensor.

QUESTIONS FOR DISCUSSION

1. Compare Newton's law of viscosity and Hooke's law of elasticity. What is the origin of these
"laws"?
2. Verify that "momentum per unit area per unit time' 7 has the same dimensions as "force per
unit area."
3. Compare and contrast the molecular and convective mechanisms for momentum trans-
port.
4. What are the physical meanings of the Lennard-Jones parameters and how can they be deter-
mined from viscosity data? Is the determination unique?
5. How do the viscosities of liquids and low-density gases depend on the temperature and pres-
sure?
6. The Lennard-Jones potential depends only on the intermolecular separation. For what kinds
of molecules would you expect that this kind of potential would be inappropriate?
7. Sketch the potential energy function <p(r) for rigid, nonattracting spheres.
8. Molecules differing only in their atomic isotopes have the same values of the Lennard-Jones
potential parameters. Would you expect the viscosity of CD to be larger or smaller than that
4
of CH at the same temperature and pressure?
4
9. Fluid A has a viscosity twice that of fluid B; which fluid would you expect to flow more
rapidly through a horizontal tube of length L and radius R when the same pressure difference
is imposed?
10. Draw a sketch of the intermolecular force F{r) obtained from the Lennard-Jones function
for <p(r). Also, determine the value of r m in Fig. 1.4-2 in terms of the Lennard-Jones para-
meters.
11. What main ideas are used when one goes from Newton's law of viscosity in Eq. 1.1-2 to the
generalization in Eq. 1.2-6?
12. What reference works can be consulted to find out more about kinetic theory of gases and liq-
uids, and also for obtaining useful empiricisms for calculating viscosity?

PROBLEMS
1A.1 Estimation of dense-gas viscosity. Estimate the 1A.2 Estimation of the viscosity of methyl fluoride. Use
viscosity of nitrogen at 68°F and 1000 psig by means of Fig. Fig. 1.3-1 to find the viscosity in Pa • s of CH F at 370°C and
3
1.3-1, using the critical viscosity from Table E.I. Give the 120 atm. Use the following values 1 for the critical con-
result in units of lb,,,/ft • s. For the meaning of "psig," see stants: T = 4.55°C, p c = 58.0 atm, p c = 0.300 g/cm .
3
c
Table F.3-2.
Answer: 1300 X 10" lb,,,/ft • s ] K. A. Kobe and R. E. Lynn, Jr., Chem. Revs. 52,117-236 (1953),
7
see p. 202.