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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}): Re = (ρ)LV/μ
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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