Page 77 - Bird R.B. Transport phenomena

62 Chapter 2 Shell Momentum Balances and Velocity Distributions in Laminar Flow

7. Show that the Hagen-Poiseuille formula is dimensionally consistent.
8. What differences are there between the flow in a circular tube of radius R and the flow in the
same tube with a thin wire placed along the axis?
9. Under what conditions would you expect the analysis in §2.5 to be inapplicable?
10. Is Stokes' law valid for droplets of oil falling in water? For air bubbles rising in benzene? For
tiny particles falling in air, if the particle diameters are of the order of the mean free path of
the molecules in the air?
11. Two immiscible liquids, A and B, are flowing in laminar flow between two parallel plates. Is
it possible that the velocity profiles would be of the following form? Explain.

Liquid A

Liquid В

12. What is the terminal velocity of a spherical colloidal particle having an electric charge e in an
electric field of strength %? How is this used in the Millikan oil-drop experiment?

PROBLEMS 2A.1 Thickness of a falling film. Water at 20°C is flowing down a vertical wall with Re = 10.
Calculate (a) the flow rate, in gallons per hour per foot of wall length, and (b) the film thickness
in inches.
Answers: (a) 0.727 gal/hr • ft; (b) 0.00361 in.
2A.2 Determination of capillary radius by flow measurement. One method for determining the
radius of a capillary tube is by measuring the rate of flow of a Newtonian liquid through the
tube. Find the radius of a capillary from the following flow data:
Length of capillary tube 50.02 cm
2
5
Kinematic viscosity of liquid 4.03 X 10~ m /s
Density of liquid 0.9552 X 10 3 kg/m 3
5
Pressure drop in the horizontal tube 4.829 X 10 Pa
Mass rate of flow through tube 2.997 X 10 3 kg/s
What difficulties may be encountered in this method? Suggest some other methods for deter-
mining the radii of capillary tubes.
2A.3 Volume flow rate through an annulus. A horizontal annulus, 27 ft in length, has an inner ra-
dius of 0.495 in. and an outer radius of 1.1 in. A 60% aqueous solution of sucrose (C H 2O )
12 2 n
is to be pumped through the annulus at 20°C. At this temperature the solution density is 80.3
lb/ft 3 and the viscosity is 136.8 lb,,,/ft • hr. What is the volume flow rate when the impressed
pressure difference is 5.39 psi?
3
Answer: 0.108 ft /s
2A.4 Loss of catalyst particles in stack gas.
(a) Estimate the maximum diameter of microspherical catalyst particles that could be lost in
the stack gas of a fluid cracking unit under the following conditions:

Gas velocity at axis of stack =1.0 ft/s (vertically upward)
Gas viscosity = 0.026 cp
Gas density = 0.045 lb/ft 3
Density of a catalyst particle = 1.2 g/cm 3
6
Express the result in microns (1 micron = 10~ = 1/xm).
(b) Is it permissible to use Stokes' law in (a)?
Answers: (a) 110 /im; Re = 0.93