fluid_mechanics
512 Chapter 9 ■ Flow over Immersed Bodies Shape Reference area Drag coefficient C D D Parachute Frontal area A = __ π D 2 4 1.4 D Porous parabolic dish Frontal area A = __ π D 2 4 Porosity 0 0.2 0.5 1.42 1.20 0.82 0.95 0.90 0.80 Porosity = open area/total area Average person Standing Sitting Crouching C D A = 9 ft 2 C D A = 6 ft 2 C D A = 2.5 ft 2 l D Fluttering flag A = D /D 1 2 3 C D 0.07 0.12 0.15 Empire State Building Frontal area 1.4 Six-car passenger train Bikes Upright commuter Racing Drafting Streamlined Frontal area A = 5.5 ft 2 A = 3.9 ft 2 A = 3.9 ft 2 A = 5.0 ft 2 1.8 1.1 0.88 0.50 0.12 Tractor-trailer trucks Standard Fairing Gap seal With fairing With fairing and gap seal Frontal area Frontal area Frontal area 0.96 0.76 0.70 U Tree U = 10 m/s U = 20 m/s U = 30 m/s Frontal area 0.43 0.26 0.20 Dolphin Wetted area 0.0036 at Re = 6 × 10 6 (flat plate has C Df = 0.0031) Large birds Frontal area 0.40 F I G U R E 9.30 (Refs. 5, 6, 15, 20). Typical drag coefficients for objects of interest
9.4 Lift 513 Denotes p > p 0 Denotes p < p 0 U, p 0 F I G U R E 9.31 an automobile. Pressure distribution on the surface of E XAMPLE 9.14 Lift from Pressure and Shear Stress Distributions GIVEN When a uniform wind of velocity U blows past the semicircular building shown in Fig. E9.14a,b, the wall shear stress and pressure distributions on the outside of the building are as given previously in Figs. E9.8b and E9.9a, respectively. FIND If the pressure in the building is atmospheric 1i.e., the value, p 0 , far from the building2, determine the lift coefficient and the lift on the roof. SOLUTION From Eq. 9.2 we obtain the lift as As is indicated in Fig. E9.14b, we assume that on the inside of the building the pressure is uniform, p p 0 , and that there is no shear stress. Thus, Eq. 1 can be written as or where b and D are the length and diameter of the building, respectively, and dA b1D22du. Equation 2 can be put into dimensionless form by using the dynamic pressure, rU 2 2, planform area, A bD, and dimensionless shear stress to give l bD 2 l p sin u dA t w cos u dA p l 1 p p 0 2 sin u b a D 2 b du c p p 1 p p 0 2 sin u du t w cos u du d 0 0 p t w cos u b a D 2 b du 0 F1u2 t w 1Re2 1 2 1rU 2 22 l 1 2 rU 2 A c 1 2 p 1 p p 0 2 sin u du 1 2 rU 2 1 21Re p F1u2 cos u du d 0 From the data in Figs. E9.8b and E9.9a, the values of the two integrals in Eq. 3 can be obtained by determining the area under the 0 0 (1) (2) (3) curves of 31p p 0 21rU 2 224 sin u versus u and F1u2 cos u versus u plotted in Figs. E9.14c and E9.14d. The results are and Thus, the lift is or and p 0 l 1 2 rU 2 A ca 1 2 b 11.762 1 21Re 13.922d C L l 1 2 rU 2 A (Ans) (4) (Ans) COMMENTS Consider a typical situation with D 20 ft, U 30 fts, b 50 ft, and standard atmospheric conditions 1r 2.38 10 3 slugsft 3 and n 1.57 10 4 ft 2 s2, which gives a Reynolds number of Re UD n 130 ft s2120 ft2 3.82 1.57 10 4 ft 2 106 s Hence, the lift coefficient is 1 p p 0 2 sin u du 1.76 1 2 rU 2 p F1u2 cos u du 3.92 0 l a0.88 1.96 1Re b a1 2 rU 2 Ab 0.88 1.96 1Re 1.96 C L 0.88 0.88 0.001 0.881 13.82 10 6 2 1 2
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512 Chapter 9 ■ Flow over Immersed Bodies<br />
Shape<br />
Reference area<br />
Drag coefficient<br />
C D<br />
D<br />
Parachute<br />
Frontal area<br />
A = __ π<br />
D 2<br />
4<br />
1.4<br />
D<br />
Porous<br />
parabolic<br />
dish<br />
Frontal area<br />
A = __ π<br />
D 2<br />
4<br />
Porosity<br />
0 0.2 0.5<br />
1.42 1.20 0.82<br />
0.95 0.90 0.80<br />
Porosity = open area/total area<br />
Average<br />
person<br />
Standing<br />
Sitting<br />
Crouching<br />
C D A = 9 ft 2<br />
C D A = 6 ft 2<br />
C D A = 2.5 ft 2<br />
l<br />
D<br />
Fluttering<br />
flag<br />
A = D<br />
/D<br />
1<br />
2<br />
3<br />
C D<br />
0.07<br />
0.12<br />
0.15<br />
Empire<br />
State Building<br />
Frontal area<br />
1.4<br />
Six-car passenger train<br />
Bikes<br />
Upright commuter<br />
Racing<br />
Drafting<br />
Streamlined<br />
Frontal area<br />
A = 5.5 ft 2<br />
A = 3.9 ft 2<br />
A = 3.9 ft 2<br />
A = 5.0 ft 2<br />
1.8<br />
1.1<br />
0.88<br />
0.50<br />
0.12<br />
Tractor-trailer trucks<br />
Standard<br />
Fairing<br />
Gap seal<br />
With fairing<br />
With<br />
fairing and<br />
gap seal<br />
Frontal area<br />
Frontal area<br />
Frontal area<br />
0.96<br />
0.76<br />
0.70<br />
U<br />
Tree<br />
U = 10 m/s<br />
U = 20 m/s<br />
U = 30 m/s<br />
Frontal area<br />
0.43<br />
0.26<br />
0.20<br />
Dolphin<br />
Wetted area<br />
0.0036 at Re = 6 × 10 6<br />
(flat plate has C Df = 0.0031)<br />
Large<br />
birds<br />
Frontal area<br />
0.40<br />
F I G U R E 9.30<br />
(Refs. 5, 6, 15, 20).<br />
Typical drag coefficients for objects of interest
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