Zaxis Isaac PD - Page 42

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Zaxis Inc. LLC
801.264.1000
2442 South 2570 West
West Valley City, UT 84119
Pressure and Density — Pressure and density are considered mechanical properties
of the uid, although they are also thermodynamic properties related to the tempera-
ture and entropy of the uid. 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 den-
sity changes are signicant in ow problems, then the ow must be considered com-
pressible. Compressibility effects result when the speed of the ow approaches the
speed of sound.
Fluid Flow — Real Fluids Equations concerning the ow of real uids are complex. In
turbulent ow, the equations are not completely known. Laminar ow 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 ow situations.
Experimentation is still important for fully correlating theory with actual ow.
Laminar vs. Turbulent Flow — When ow velocity increases, the ow becomes
unstable, and changes from laminar to turbulent ow. In turbulent ow, gas particles
start moving in highly irregular and difcult-to-predict paths. Eddies form transfers
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 ow are more complex than the formulas for laminar ow. For most answers,
they require empirical relations derived from controlled experiments.
Whether a ow is laminar or turbulent generally can be determined by calculating the
Reynolds number (Re) of the ow. The Reynolds number is the product of the densi-
ty (designated by the Greek lower-case letter rho {ρ}), a characteristic length L, and
a characteristic velocity v, all divided by the coefcient of viscosity (designated by the
Greek lower-case letter mu {μ}):
Re = (ρ) Lv/μ
Reynolds Number (Re) — The Reynolds number has no unit of measure; it is a pure
number. As long as Reynolds number is small, the ow remains laminar. When the
Reynolds number becomes greater than a critical value, the ow becomes turbulent.
With rho {ρ}, L, and mu {μ} constant, Re varies simply as velocity changes. For ow
in smooth round pipes, critical value is about 2,000, with L equal to the diameter of the
pipe.