Page 193 - Bird R.B. Transport phenomena

Chapter 6

Interphase Transport

in Isothermal Systems

§6.1 Definition of friction factors

§6.2 Friction factors for flow in tubes
§6.3 Friction factors for flow around spheres
§6.4° Friction factors for packed columns

In Chapters 2-4 we showed how laminar flow problems may be formulated and solved.
In Chapter 5 we presented some methods for solving turbulent flow problems by dimen-
sional arguments or by semiempirical relations between the momentum flux and the
gradient of the time-smoothed velocity. In this chapter we show how flow problems can
be solved by a combination of dimensional analysis and experimental data. The tech-
nique presented here has been widely used in chemical, mechanical, aeronautical, and
civil engineering, and it is useful for solving many practical problems. It is a topic worth
learning well.
Many engineering flow problems fall into one of two broad categories: flow in chan-
nels and flow around submerged objects. Examples of channel flow are the pumping of
oil through pipes, the flow of water in open channels, and extrusion of plastics through
dies. Examples of flow around submerged objects are the motion of air around an air-
plane wing, motion of fluid around particles undergoing sedimentation, and flow across
tube banks in heat exchangers.
In channel flow the main object is usually to get a relationship between the vol-
ume rate of flow and the pressure drop and/or elevation change. In problems involv-
ing flow around submerged objects the desired information is generally the relation
between the velocity of the approaching fluid and the drag force on the object. We
have seen in the preceding chapters that, if one knows the velocity and pressure dis-
tributions in the system, then the desired relationships for these two cases may be ob-
tained. The derivation of the Hagen-Poiseuille equation in §2.3 and the derivation of
the Stokes equation in §2.6 and §4.2 illustrate the two categories we are discussing
here.
For many systems the velocity and pressure profiles cannot be easily calculated, par-
ticularly if the flow is turbulent or the geometry is complicated. One such system is the
flow through a packed column; another is the flow in a tube in the shape of a helical coil.
For such systems we can take carefully chosen experimental data and then construct
"correlations" of dimensionless variables that can be used to estimate the flow behavior
in geometrically similar systems. This method is based on §3.7.

177