460 10 Transport Processesflow is not laminar, do you think the speed would be
greater or less than expected with laminar flow?10.15An Ostwald viscometer consists of a capillary tube
through which a fixed volume of a liquid is allowed to
flow under hydrostatic pressure. If in a certain viscometer
the fixed volume of water requires 215.3 s to flow at
20 ◦C, calculate the time required for this volume of
sulfuric acid to flow at 20◦C. Use the fact that the
hydrostatic force in a given viscometer is proportional to
the density of the liquid. The density of sulfuric acid is
1.834 g mL−^1 and that of water is 0.9982 g mL−^1 at 20◦C.
10.16In a certain Ostwald viscometer (see Problem 10.15), a
fixed volume of water required 183.5 s to flow at 20◦C. If
the same volume of mercury flows in 20.78 s at 20◦C, find
the viscosity of mercury at 20◦C. The density of water is
0.99823 g mL−^1 , and that of mercury is 13.5462 g mL−^1.
10.17In experiments with a certain Ostwald viscometer, a time
of 56.8 s is required for the specified volume of water to
flow at 20.0◦C. Find the time required for the same
volume of ethanol to flow. The density of ethanol is
0.7893 g mL−^1 at this temperature, and that of water is
0.9982 g mL−^1. The viscosity of water is
- 002 × 10 −^3 kg m−^1 s−^1 at this temperature and that of
ethanol is 1. 200 × 10 −^3 kg m−^1 s−^1.
10.18Thepoise(g cm−^1 s−^1 ) is the cgs unit of viscosity. The
viscosity of dry air is given in poise as a function of
temperature by the following formula:^4
η(
1345. 8 × 10 −^7)
T^3 /^2
T+ 110. 4where units are disregarded in the formula. Estimate the
steady-state speed of a basketball falling in air at 25◦C,
assuming laminar flow. The circumference of a standard
U.S. basketball is 30 inches, and its mass is between 20
and 22 ounces. Does your answer seem reasonable? If
not, explain why it is not.
10.19 a.A certain garden hose is advertised to be able to
deliver 550 gallons of water per hour. If the hose if 50
feet long and has an inside diameter of 5/8 inch,
estimate the water pressure necessary to deliver this
much water, assuming laminar flow.
b.Calculate the Reynolds number for the flow in part a,
and determine whether the flow is laminar.
10.20Water at 298.15 K is flowing through a tube of length
50.0 cm and radius 0.400 cm. The pressure difference
between the two ends is 0.750 atm.
a.Find the volume of water that flows through the tube
in 1.00 minute assuming laminar flow.
b.Calculate the Reynolds number and determine
whether the flow is laminar.
10.21 a.Using the equation of continuity, show for a diffusing
system in a steady state that the concentration gradient
must be uniform if the diffusion coefficient is a
constant and if the cross-sectional area of the system
is uniform.
b.Argue that the temperature gradient must be uniform
in a system of uniform cross section with a uniform
thermal conductivity if a steady state occurs.10.3 The Gas Kinetic Theory of Transport
Processes in Hard-Sphere Gases
An elementary molecular theory for nonequilibrium processes in a hard-sphere gas can
be based on the gas kinetic theory that was presented in Chapter 9. We will apply this
theory to self-diffusion and give the results of its application to heat conduction and
viscous flow.Self-Diffusion in a Hard-Sphere Gas
For diffusion to take place there must be at least two substances present.Self-diffusion
is a model diffusion process in which the molecules of the two substances have all of
their properties in common but can somehow be distinguished from each other. This(^4) Tables of Thermal Properties of Gases, Table 1-B, U.S. Natl. Bur. Stand. Circ. 564, U.S. Government Printing Office, Washington, DC, 1955.