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Fluids vs. Solids
The distinguishing feature of a fluid (gas or liquid), in contrast to a solid, is how
easily the fluid can be deformed. If a shearing force, even a very small force, is applied to a fluid, the
fluid will move and continue to move as long as the shear acts on it. For example, the force of gravity
causes water poured from a cup to flow. Water continues to flow as long as the cup is tilted. If the cup
is turned back up, the flow stops. The wall of the cup has balanced the forces.
Gas vs. Liquid
Unlike liquids, gases cannot be poured as easily from one open container into
another, but they deform under shear stress just the same. Because shear stresses result from 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. However, if density changes are significant in flow problems,
then the flow must be considered compressible. Compressibility effects result 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 {
ρ
}), a characteristic length L, and a characteristic velocity v, all divided by the coefficient
of viscosity (designated by the Greek lower-case letter mu {
μ
}):
