drag & lift solved problems - philadelphia university · lift force on body: a s bc p = = 6....

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09/12/2010 09/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1 1 SOLVED PROBLEMS CHAPTER (11) DRAG & LIFT

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Page 1: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 11

SOLVED PROBLEMS

CHAPTER (11)

DRAG & LIFT

Page 2: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 22

SUMMARY

1. Drag Force on Body:

2. Drag force on body is a combination of Form Drag (Pressure

Forces) and Skin Friction Drag (Shear Stress Forces).

3. Coefficient of a Drag of a Sphere For Re<0.5 (Stokes Drag):

4. Frequency of vortex Shedding is Given by (St = Strouhal) Number:

Page 3: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 33

5. Lift Force on Body: cbSAp ==

6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip

effect):

7. Drag Coefficient Corresponding to the Minimum Induced Drag:

8. Streamlining at high Re reduces the drag due to pressure and increase

the viscous drag.

9. Streamlining at Low Re increases the drag due to viscous forces.

Page 4: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

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Problem (11.7)

h=75m

D=2.5m

DF

Page 5: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 55

Problem (11.17)

D=0.5msmV 3=

Page 6: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

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Problem (11.20)

VFPPower ×==

Page 7: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 77

Problem (11.27)

Page 8: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 88

Problem 11.33 (p. 476)Problem 11.33 (p. 476)

Page 9: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 99

Problem (11.33)

25% reduction in drag when vanes introduced

Given projected area (Ap)=8.36 m2

CD without vanes = 0.78

V=100 km/hr

Page 10: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1010

Problem (11.38)

IbfWSPHERE 27=

Sphere diameter = 1 ft

S.G = 0.85

?min =alTerV

Page 11: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1111

Problem (11.38)

Page 12: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1212

Problem (11.49)

L=80 cm, d = 20 cm

Weight = 200 N

?min =alTerV

Page 13: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1313

Problem (11.49)

Page 14: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 1414

Problem (11.73)

( )( ) 4.1

2.18

=

=

StallingL

LandingL

C

CspeedstallingthanfastersmisspeedLanding

Page 15: DRAG & LIFT SOLVED PROBLEMS - Philadelphia University · Lift Force on Body: A S bc p = = 6. Lift Coefficient For a Symmetric Two – Dimensional Wing (No tip effect): 7. Drag Coefficient

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THE END