the no-slip condition, and the thin boundary layer in which the viscous
effects are significant near the plate surface is the viscous flow region. The
region of flow on both sides away from the plate and unaffected by the
presence of the plate is the inviscid flow region.
Internal versus External Flow
A fluid flow is classified as being internal or external, depending on
whether the fluid is forced to flow in a confined channel or over a surface.
The flow of an unbounded fluid over a surface such as a plate, a wire, or a
pipe is external flow. The flow in a pipe or duct is internal flow if the fluid
is completely bounded by solid surfaces. Water flow in a pipe, for example,
is internal flow, and airflow over a ball or over an exposed pipe during a
windy day is external flow (Fig. 1–16). The flow of liquids in a duct is
called open-channel flow if the duct is only partially filled with the liquid
and there is a free surface. The flows of water in rivers and irrigation
ditches are examples of such flows.
Internal flows are dominated by the influence of viscosity throughout the
flow field. In external flows the viscous effects are limited to boundary layers
near solid surfaces and to wake regions downstream of bodies.
Compressible versus Incompressible Flow
A flow is classified as being compressible or incompressible, depending on
the level of variation of density during flow. Incompressibility is an approximation,
and a flow is said to be incompressible if the density remains
nearly constant throughout. Therefore, the volume of every portion of fluid
remains unchanged over the course of its motion when the flow (or the
fluid) is incompressible.
The densities of liquids are essentially constant, and thus the flow of liquids
is typically incompressible. Therefore, liquids are usually referred to as
incompressible substances. A pressure of 210 atm, for example, causes the
density of liquid water at 1 atm to change by just 1 percent. Gases, on the
other hand, are highly compressible. A pressure change of just 0.01 atm, for
example, causes a change of 1 percent in the density of atmospheric air.
When analyzing rockets, spacecraft, and other systems that involve highspeed
gas flows, the flow speed is often expressed in terms of the dimensionless
Mach number defined as