Reference 8-49
relative motion, stresses are equivalent whether the fluid flows past a stationary
object or the object moves through the fluid.
Although a fluid can deform easily under an applied force, the fluid’s viscosity
creates resistance to this force. The viscosity of gases, which is much less than that
of liquids, increases slightly as the temperature increases, whereas that of liquids
decreases when the temperature increases. Fluid mechanics is mostly concerned
with Newtonian fluids, or those in which stress, viscosity, and rate of strain are
linearly related.
Pressure and Density
Pressure and density are considered mechanical properties of the fluid, although
they are also thermodynamic properties related to the temperature and entropy of
the fluid. For a small change in pressure, the density of a gas is essentially
unaffected. For this reason, gas and all liquids can be considered incompressible. If
density changes are significant in flow problems, however, then the flow must be
considered compressible. Compressibility affects results when the speed of the
flow approaches the speed of sound.
Fluid Flow-Real Fluids
Equations concerning the flow of real fluids are complex. In turbulent flow, the
equations are not completely known. Laminar flow is described by the Navier-
Stokes equations, for which answers can be derived only in simple cases. Only by
using large computers can answers be derived in more complex flow situations.
Experimentation is still important for fully correlating theory with actual flow.
Laminar vs. Turbulent Flow
When flow velocity increases, the flow becomes unstable, and changes from
laminar to turbulent flow. In turbulent flow, gas particles start moving in highly
irregular and difficult-to-predict paths. Eddies form and transfer momentum over
distances varying from a few millimeters, as in controlled laboratory experiments,
to several meters, as in a large room or other structure. Equations for turbulent
flow are more complex than the formulas for laminar flow. For most answers, they
require empirical relations derived from controlled experiments.
Whether a flow is laminar or turbulent generally can be determined by calculating
the Reynolds number (Re) of the flow. The Reynolds number is the product of the
density (designated by the Greek lower-case letter rho {D}), a characteristic length
L, and a characteristic velocity v, all divided by the coefficient of viscosity
(designated by the Greek lower-case letter mu {:}): Re = (D)LV/:
Reynolds Number (Re)
The Reynolds number is dimensionless, a pure number. As long as Re is small, the
flow remains laminar. When the Reynolds number becomes greater than a critical
value, the flow becomes turbulent. With rho, L, and mu constant, Re varies simply
as velocity changes. For flow in smooth round pipes, critical value is about 2,000,
with L equal to the diameter of the pipe.
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