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7/25/2019 Drag and Lift Lecture
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ME 116 Fluid Mechanics
Chapter 9: External Flows
Fall 2014
Deify Law
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External Flows Flow over bodies that are immersed in a fluid.
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_02.htmhttp://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_01b.htm7/25/2019 Drag and Lift Lecture
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Lift and Drag
Wall shear stress, , due to viscous effects Normal stress,p, due to the pressure effects
w
Pressure Force
Viscous Force
Resultant Force
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_04.htm7/25/2019 Drag and Lift Lecture
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Lift and Drag at a Surface at
Arbitrary Angle
cos sin
sin cos
x w
y w
dF pdA dA
dF pdA dA
cos sin
sin cos
x w
y w
D dF p dA dA
L dF p dA dA
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_05.htm7/25/2019 Drag and Lift Lecture
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Lift and Drag of Plate at an Angle
cos sin
sin cos
x w
y w
D dF p dA dA
L dF p dA dA
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_e02.htm7/25/2019 Drag and Lift Lecture
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Lift Coefficient and
Drag Coefficient
Lift Coefficient:
Drag Coefficient
21
2
L
LC
U A
21
2
D
DC
U A
A can be
Frontal area
or
Planform area
depending onthe geometry
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/figun_09_p466b.htm7/25/2019 Drag and Lift Lecture
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Boundary Layer Flows
Very Low Reynolds Number~ Stokes Flow
Low Reynolds Number
High Reynolds Number
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_06.htm7/25/2019 Drag and Lift Lecture
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Flow Past a Circular Cylinder
Very Low Reynolds Number
~ Stokes Flow
Low Reynolds Number
High Reynolds Number
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_07.htm7/25/2019 Drag and Lift Lecture
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Drag
Friction Drag (Drag due to shear stress)
Pressure Drag (Drag due to pressure)
21
2
, Re, , /
D
D
DragC
U A
C shape Ma l
21
2
f DfD U blC
21cos
2p DpD p dA U blC
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_05.htm7/25/2019 Drag and Lift Lecture
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Pressure Drag Coefficient
Cpis the pressure coefficient
2 2
cos cos
1 1
2 2
pp
Dp
p dA C dADC
AU A U A
21
2
o
p
p pC
U
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Drag Coefficient vs. Reynolds
Number
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_23.htm7/25/2019 Drag and Lift Lecture
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Drag Coefficient vs. Reynolds
Number for a Cylinder and a
Sphere
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_21b.htm7/25/2019 Drag and Lift Lecture
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Drag Coefficient as a Function of
Mach Number
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Drag Coefficient vs. Mach Number
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_25.htm7/25/2019 Drag and Lift Lecture
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http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_29.htmhttp://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_31.htm7/25/2019 Drag and Lift Lecture
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http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_31.htm7/25/2019 Drag and Lift Lecture
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Drag Coefficient versus
Aerodynamic Body (Car)
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Composite Drag
http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_e14.htm7/25/2019 Drag and Lift Lecture
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Effects of Angle of Attack on Lift
and Drag Coefficients