fluid_mechanics

9.3 Drag 497
1.0
0.5
1.0
C p = _____ p - p o
1_ ρ U 2
2
0
-0.5
θ
C p cos
0.5
0
-1.0
-0.5
-1.5
0
100
10
C D
1.0
30 60 90 120 150 180
θ, degrees
(a)
Experimental value
Eq. 2
0
π__
4
π__
2
θ, rad
(b)
___ 3 π
4
π
0.1
10 0
10 1
10 2
10 3
10 4
10 5
10 6
Re = UD ___
v
(c)
F I G U R E E9.9
COMMENT It is of interest to compare the friction drag to
the total drag on the cylinder. That is,
d f
d C Df 5.93 1Re
C D 15.93 1Re2 1.17 1
1 0.1971Re
For Re 10 3 , 10 4 , and 10 5 this ratio is 0.138, 0.0483, and 0.0158,
respectively. Most of the drag on the blunt cylinder is pressure
drag—a result of the boundary layer separation.
V9.7 Skydiving
practice
The drag coefficient
may be based on
the frontal area or
the planform area.
9.3.3 Drag Coefficient Data and Examples
As was discussed in previous sections, the net drag is produced by both pressure and shear stress
effects. In most instances these two effects are considered together, and an overall drag coefficient,
C D , as defined in Eq. 9.36 is used. There is an abundance of such drag coefficient data available
in the literature. This information covers incompressible and compressible viscous flows past objects
of almost any shape of interest—both man-made and natural objects. In this section we consider
a small portion of this information for representative situations. Additional data can be obtained
from various sources 1Refs. 5, 62.
Shape Dependence. Clearly the drag coefficient for an object depends on the shape of
the object, with shapes ranging from those that are streamlined to those that are blunt. The drag
on an ellipse with aspect ratio /D, where D and / are the thickness and length parallel to the
flow, illustrates this dependence. The drag coefficient C D d1rU 2 bD22, based on the frontal
area, A bD, where b is the length normal to the flow, is as shown in Fig. 9.19. The more blunt
the body, the larger the drag coefficient. With /D 0 1i.e., a flat plate normal to the flow2 we
obtain the flat plate value of C D 1.9. With /D 1 the corresponding value for a circular cylinder
is obtained. As /D becomes larger the value of C D decreases.
For very large aspect ratios 1/D S 2 the ellipse behaves as a flat plate parallel to the flow.
For such cases, the friction drag is greater than the pressure drag, and the value of C D based on the
frontal area, A bD, would increase with increasing /D. 1This occurs for larger /D values than
those shown in the figure.2 For such extremely thin bodies 1i.e., an ellipse with /D S , a flat plate,
or very thin airfoils2 it is customary to use the planform area, A b/, in defining the drag coefficient.