fluid_mechanics

514 Chapter 9 ■ Flow over Immersed Bodies
U
p 0
U
p 0
pdA
τw dA
p 0 dA
~ U 2 being of secondary importance. Hence, as indicated by the figure in the margin, for a given airfoil
dθ
(a)
(b)
1.0
0.5
0
6
–0.5
4
–1.0
2
–1.5 0
0 π__ π__ ___ 3 π π 0 π__ π__ ___ 3 π π
4 2 4
4 2 4
θ, rad θ, rad
(c)
(d)
F I G U R E E9.14
Note that the pressure contribution to the lift coefficient is or
0.88 whereas that due to the wall shear stress is only
1.961Re 12 2 0.001. The Reynolds number dependency of C L is
l 944 lb
quite minor. The lift is pressure dominated. Recall from Example
There is a considerable tendency for the building to lift off the
9.9 that this is also true for the drag on a similar shape.
From Eq. 4 with A 20 ft 50 ft 1000 ft 2
ground. Clearly this is due to the object being nonsymmetrical.
, we obtain the
The lift force on a complete circular cylinder is zero, although
lift for the assumed conditions as
the fluid forces do tend to pull the upper and lower halves
l 1 2rU 2 AC L 1 2 10.00238 slugsft 3 2130 fts2 2 11000 ft 2 210.8812 apart.
A typical device designed to produce lift does so by generating a pressure distribution that
is different on the top and bottom surfaces. For large Reynolds number flows these pressure distributions
are usually directly proportional to the dynamic pressure, rU 2 2, with viscous effects
the lift is proportional to the square of the airspeed. Two airfoils used to produce lift are indicated
in Fig. 9.32. Clearly the symmetrical one cannot produce lift unless the angle of attack, a, is nonzero.
Because of the asymmetry of the nonsymmetric airfoil, the pressure distributions on the upper and
U
lower surfaces are different, and a lift is produced even with a 0. Of course, there will be a
certain value of a 1less than zero for this case2 for which the lift is zero. For this situation, the
pressure distributions on the upper and lower surfaces are different, but their resultant 1integrated2
pressure forces will be equal and opposite.
Since most airfoils are thin, it is customary to use the planform area, A bc, in the definition
of the lift coefficient. Here b is the length of the airfoil and c is the chord length—the length
from the leading edge to the trailing edge as indicated in Fig. 9.32. Typical lift coefficients so defined
are on the order of unity. That is, the lift force is on the order of the dynamic pressure times
the planform area of the wing, l 1rU 2 22A. The wing loading, defined as the average lift per
unit area of the wing, lA, therefore, increases with speed. For example, the wing loading of the
C p sin θ = _______
p – p 0
sin θ
F( θ) cos θ
θ
D/2