Fluid Mechanics-Viscous Flow in Pipes

In the previous chapters we have considered a variety of topics concerning the motion of
fluids. The basic governing principles concerning mass, momentum, and energy were developed
and applied, in conjunction with rather severe assumptions, to numerous flow situations.
In this chapter we will apply the basic principles to a specific, important topic—the
flow of viscous, incompressible fluids in pipes and ducts.
The transport of a fluid 1liquid or gas2 in a closed conduit 1commonly called a pipe if
it is of round cross section or a duct if it is not round2 is extremely important in our daily
operations. A brief consideration of the world around us will indicate that there is a wide variety
of applications of pipe flow. Such applications range from the large, man-made Alaskan
pipeline that carries crude oil almost 800 miles across Alaska, to the more complex 1and certainly
not less useful2 natural systems of “pipes” that carry blood throughout our body and
air into and out of our lungs. Other examples include the water pipes in our homes and the
distribution system that delivers the water from the city well to the house. Numerous hoses
and pipes carry hydraulic fluid or other fluids to various components of vehicles and machines.
The air quality within our buildings is maintained at comfortable levels by the distribution
of conditioned 1heated, cooled, humidifieddehumidified2 air through a maze of
pipes and ducts. Although all of these systems are different, the fluid-mechanics principles
governing the fluid motions are common. The purpose of this chapter is to understand the
basic processes involved in such flows.
Some of the basic components of a typical pipe system are shown in Fig. 8.1. They include
the pipes themselves 1perhaps of more than one diameter2, the various fittings used to
connect the individual pipes to form the desired system, the flowrate control devices 1valves2,
and the pumps or turbines that add energy to or remove energy from the fluid. Even the most
simple pipe systems are actually quite complex when they are viewed in terms of rigorous
analytical considerations. We will use an “exact” analysis of the simplest pipe flow topics 1such as laminar flow in long, straight, constant diameter pipes2 and dimensional analysis
considerations combined with experimental results for the other pipe flow topics. Such an
approach is not unusual in fluid mechanics investigations. When “real world” effects are
important 1such as viscous effects in pipe flows2, it is often difficult or “impossible” to use
only theoretical methods to obtain the desired results. A judicious combination of experimental
data with theoretical considerations and dimensional analysis often provides the desired
results. The flow in pipes discussed in this chapter is an example of such an analysis.