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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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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.htm

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http://www.wiley.com/college/munson/0470262842/image_gallery/ch09/pages/fig_09_31.htm

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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.htm

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Effects of Angle of Attack on Lift

and Drag Coefficients