Page 198 - Introduction to Naval Architecture

184 RESISTANCE

Figure 8.6 Laminar and turbulent flow

which breakdown of laminar flow occurs depends upon the smoothness
of the surface and the initial turbulence present in the fluid. For a
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smooth fiat plate it occurs at a Reynolds' number between 3 X 10 and
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10 . In turbulent flow the boundary layer still exists but in this case,
besides the molecular friction force there is an interaction due to
momentum transfer of fluid masses between adjacent layers. The
transition from one type of flow to the other is a matter of stability of
flow. At low Reynolds' numbers, disturbances die out and the flow is
stable. At the critical value the laminar flow becomes unstable and the
slightest disturbance will create turbulence. The critical Reynolds'
number for a flat plate is a function of the distance, /, from the leading
edge and is given by:

Ahead of the point defined by / the flow is laminar. At / transition begins
and after a transition region turbulence is fully established. For a flat
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plate the critical Reynolds' number is about 10 . A curved surfece is
subject to a pressure gradient and this has a marked affect on
transition. Where pressure is decreasing transition is delayed. The
thickness of the turbulent boundary layer is given by:

where L is the distance from the leading edge and R L is the
corresponding Reynolds' number.
Even in turbulent flow the fluid particles in contact with the surface
are at rest relative to the surface. There exists a very thin laminar sub-
layer. Although thin, it is important as a body appears smooth if the
surface roughness does not project through this sub-layer. Such a body
is said to be hydraulically smooth.
The existence of two flow regimes is important for model tests
conducted to determine a ship's resistance. If the model is too small it