fluid_mechanics

9.4 Lift 511
D
Shape
Solid
hemisphere
Reference area
A
A = __ π
D 2
4
Drag coefficient
C D
1.17
0.42
Reynolds number
Re = ρUD/
μ
Re > 10 4
D
Hollow
hemisphere
A = __ π
D 2
4
1.42
0.38
Re > 10 4
D
Thin disk
A = __ π
D 2
4
1.1
Re > 10 3
D
Circular
rod
parallel
to flow
A = __ π
D 2
4
/D
0.5
1.0
2.0
4.0
C D
1.1
0.93
0.83
0.85
Re > 10 5
θ, degrees C D
θ
D
Cone
A = __ π
D 2
4
10
30
60
90
0.30
0.55
0.80
1.15
Re > 10 4
D
Cube
A = D 2
1.05
Re > 10 4
D
Cube
A = D 2
0.80
Re > 10 4
D
A = __ π
D 2
4
0.04
Re > 10 5
Streamlined
body
F I G U R E 9.29
objects (Ref. 5).
Typical drag coefficients for regular three-dimensional
Usually most lift
comes from pressure
forces, not viscous
forces.
Most common lift-generating devices 1i.e., airfoils, fans, spoilers on cars, etc.2 operate in the
large Reynolds number range in which the flow has a boundary layer character, with viscous effects
confined to the boundary layers and wake regions. For such cases the wall shear stress, t w ,
contributes little to the lift. Most of the lift comes from the surface pressure distribution. A typical
pressure distribution on a moving car is shown in Fig. 9.31. The distribution, for the most part,
is consistent with simple Bernoulli equation analysis. Locations with high-speed flow 1i.e., over
the roof and hood2 have low pressure, while locations with low-speed flow 1i.e., on the grill and
windshield2 have high pressure. It is easy to believe that the integrated effect of this pressure distribution
would provide a net upward force.
For objects operating in very low Reynolds number regimes 1i.e., Re 6 12, viscous effects
are important, and the contribution of the shear stress to the lift may be as important as that of the
pressure. Such situations include the flight of minute insects and the swimming of microscopic organisms.
The relative importance of t w and p in the generation of lift in a typical large Reynolds
number flow is shown in Example 9.14.