NAVWEPS CO-SOT-80 
BASIC AE,RODYNAMlCS 
the turbulent area, a sharp “crackling” will 
be audible. 
In order to compare the characteristics of 
the laminar and turbulent boundary layers, the 
velocity profiles (the variation of boundary 
layer velocity with height above the surface) 
should be compared under conditions which 
could produce either laminar or turbulent 
flow. The typical laminar and turbulent pro- 
files are shown in figure 1.24. The velocity 
profile of the turbulent boundary layer shows 
a much sharper initial change of velocity but 
a greater height (or boundary layer thickness) 
required to reach the free stream velocity. 
As a result of these differences, a comparison 
will show: 
(1) The turbulent boundary layer has a 
fuller velocity profile and has higher local 
velocities immediately adjacent to the sur- 
face. The turbulent boundary layer has 
higher kinetic energy in the airflow next to 
the surface. 
(2) At the surface, the laminar boundary 
layer has the less rapid change of velocity 
with distance above the plate. Since the 
shearing stress is proportional to the velocity 
gradient, the lower velocity gradient of the 
laminar boundary layer is evidence of a 
lower friction drag on the surface. If the 
conditions of flow were such that either a 
turbulent or a laminar boundary layer could 
exist, the laminar skin friction would be 
about one-third that for turbulent flow. 
The low friction drag of the laminar bound- 
ary layer makes it quite desirable. However, 
the transition tends to take place in a natural 
fashion and limit the extensive development 
of the laminar boundary layer. 
REYNOLDS NUMBER. Whether a lam- 
inar or turbulent boundary layer exists depends 
on the combined effects of velocity, viscosity, 
distance from the leading edge, density, etc. 
The effect of the most important factors is 
combined in a dimensionless parameter called 
“Reynolds Number, RN.” The Reynolds 
Number is a dimensionless ratio which por- 
trays the relative magnitude of dynamic and 
viscous forces in the flow. 
where 
RiV=Reynolds Number, dimensionless 
V= velocity, ft. per sec. 
x= distance from leading edge, ft. 
Y= kinematic viscosity, sq. ft. per sec. 
While the actual magnitude of the Reynolds 
Number has no physical significance, the 
quantity is used as an index to predict and 
correlate various phenomena of viscous fluid, 
flow. When the RN is low, viscous or fric- 
tion forces predominate; when the RN is high, 
dynamic or inertia forces predominate. The 
effect of the variables in the equation for 
Reynolds Number should be understood. The 
RN varies directly with velocity and distance 
back from the leading edge and inversely with 
kinematic viscosity. High RN’s are obtained 
with large chord surfaces, high velocities, and 
low altitude; low RN’sresult from small chord 
surfaces, low velocities, and high altitudes- 
high altitudes producing high values for kine- 
matic viscosity. 
The most direct use of Reynolds Number is 
the indexing or correlating the skin friction 
drag of a surface. Figure 1.25 illustrates the 
variation of the friction drag of a smooth, 
flat plate with a Reynolds Number which is 
based on the length or chord of the plate. 
The graph shows separate lines of drag coeffi- 
cient if the flow should be entirely laminar or 
entirely turbulent. The two curves for lam- 
inar and turbulent friction drag illustrate the 
relative magnitude of friction drag coefficient 
if either type of boundary layer could exist. 
The drag coefficients for either laminar or tur- 
bulent flow decrease with increasing RN since 
the velocity gradient decreases as the boundary 
layer thickens.