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09/12/201009/12/2010 Dr. Munzer Ebaid Dr. Munzer Ebaid 11
CHAPTER (11)
DRAG & LIFT
DR. MUNZER EBAID
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Vortex Shedding From Cylindrical Bodies
If the frequency of the vortex shedding is in resonance with thenatural frequency of the member that produce it, large amplitude of vibration with resulting large stresses can develop.
Experiments show that the Frequency of Shedding is given in terms of Strouhal Number (st).
Vortex Shedding
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Strouhal Number versus Reynolds number for flow past a circular cylinder.
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Example (11.2)
5100.7 ×=eR
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Effect of Streamlining
310>eRFor the drag of a cylinder is predominantly due to pressure variation around the cylinder caused largely to Separation. Hence, if the separation can be eliminated, the drag will be reduced.
When a body is streamlined by elongating it and reducing its curvature, the pressure drag is reduced. However, viscous forces are increased because the surface is increased.
The optimum condition for streamlining is when the sum of surface drag and pressure drag is minimum.
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Effect of StreamliningStreamlining at high Re reduces the drag due to pressure and increase the viscous drag.
Streamlining at Low Re <1 increases the drag due to viscous forces.
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Example (11.3)
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Drag of Axisymmetric and Three – dimensional Bodies
Stokes’ Law, for a Sphere, and for Laminar Flow: (Re<0.5)
Combining Eqns (11.8) & (11.6), we get
Correlation proposed by Clift and Gauvin For (Re) up to 5103×
Eqn (11.10) deviates from the standard curve (next slide) from (-4% to 6%) for Reynolds numbers up to 5103×
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Figure 11.11 (p. 448)Coefficient of drag versus Reynolds number for Axisymetric Bodies. [Data sources: Abbott (9), Brevoortand Joyner (10), Freeman (11) and Rouse (12)]
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Approximate (CD) Values for Various Bodies at Reynolds numbers
)10(Re 4>
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Example (11.4)
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Example (11.5)
?max =V
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END OF LECTURE (2)
