1. Pharos University ME 253 Fluid Mechanics II
Flow over bodies; Lift and Drag

2. External External Flows
Bodies in motion, experience fluid forces and moments.
Examples include: aircraft, automobiles, buildings, ships, submarines, turbo machines.
Fuel economy, speed, acceleration, stability, and control are related to the forces and moments.
Airplane in level steady flight:
drag = thrust & lift = weight.

3. Flow over immersed bodies
flow classification:
2D, axisymmetric, 3D
bodies:
streamlined and blunt

4. Lower surface (underside of wing): high pressure
Airplane
Upper surface
(upper side of wing):
low pressure
Lower surface (underside of wing): high pressure

5. Lift and Drag shear stress and pressure integrated over body surface
drag: force component in the direction of upstream velocity
lift: force normal to upstream velocity

6. AIRFOIL NOMENCLATURE Mean Chamber Line: Points halfway between upper
and lower surfaces
Leading Edge: Forward point of mean chamber line
Trailing Edge: Most reward point of mean chamber line
Chord Line: Straight line connecting the leading and trailing edges
Chord, c: Distance along the chord line from leading to trailing edge
Chamber: Maximum distance between mean chamber line
and chord line

7. AERODYNAMIC FORCE Relative Wind: Direction of V∞
We used subscript ∞ to indicate far upstream conditions
Angle of Attack, a: Angle between relative wind (V∞) and chord line
Total aerodynamic force, R, can be resolved into two force components
Lift, L: Component of aerodynamic force perpendicular to relative wind
Drag, D: Component of aerodynamic force parallel to relative wind

8. Pressure Forces acting on the Airfoil
Low Pressure
High velocity
High Pressure
Low velocity
Low Pressure
High velocity
High Pressure
Low velocity
Bernoulli’s equation says where pressure is high, velocity will be
low and vice versa.

9. Relationship between L´ and pV

10. Relationship between L´ and p (Continued)
Divide left and right sides by
We get:

11. Pressure Coefficient Cp
From the previous slide,
The left side was previously defined as the sectional lift
coefficient Cl.
The pressure coefficient is defined as:
Thus,

12. Drag: component parallel to flow direction.
Fluid dynamic forces are due to pressure and viscous forces.
Drag: component parallel to flow direction.
Lift: component normal to flow direction.

13. Lift and drag forces can be found by integrating pressure and wall-shear stress.
Drag and Lift

14. Drag and Lift Lift FL and drag FD forces fn (  , A,V )
Dimensional analysis: lift and drag coefficients.
Area A can be frontal area (drag applications), plan form area (wing aerodynamics).

15. Example: Automobile Drag bile Drag
CD = 1.0, A = 2.5 m2, CDA = 2.5m2
CD = 0.28, A = 1 m2, CDA = 0.28m2
Drag force FD=1/2V2(CDA) will be ~ 10 times larger for Scion XB
Source is large CD and large projected area
Power consumption P = FDV =1/2V3(CDA) for both scales with V3!

16. Drag and Lift If CL and CD fn of span location x.
A local CL,x and CD,x are introduced.
The total lift and drag is determined by integration over the span L

17. Friction and Pressure Drag
Fluid dynamic forces: pressure and friction effects.
FD = FD,friction + FD,pressure
CD = CD,friction + CD,pressure
Friction drag
Pressure drag
Friction & pressure drag

18. Flow Around Objects

19. Streamlining Streamlining reduces drag by reducing FD,pressure,
Eliminate flow separation and minimize total drag FD

20. Streamlining

21. CD of Common Geometries
For many shapes, total drag CD is constant for Re > 104

22. CD of Common Geometries

23. CD of Common Geometries

24. Flat Plate Drag
Drag on flat plate is due to friction created by laminar,
transitional, and turbulent boundary layers.

25. Flat Plate Drag Local friction coefficient
Laminar:
Turbulent:
Average friction coefficient

26. Cylinder and Sphere Drag

27. Cylinder and Sphere Drag
Flow is strong function of Re.
Wake narrows for turbulent flow since turbulent boundary layer is more resistant to separation.
sep, lam ≈ 80º
sep,Tur ≈ 140º

28. Lift
Lift is the net force (due to pressure and viscous forces) perpendicular to flow direction.
Lift coefficient
A=bc is the planform area

29. Characteristics of Cl vs. a
Stall Cl
Slope= 2p if a is in radians.
a = a0
Angle of
zero lift
Angle of Attack, a in degrees
or radians

30. EXAMPLE: AIRFOIL STALL
Lift
Angle of Attack, a

31. Effect of Angle of Attack
CL≈2 for  < stall
Lift increases linearly with 
Objective:Maximum CL/CD
CL/CD increases until stall.

32. Thickness and camber affects pressure distribution and
location of flow separation.
Effect of Foil Shape

33. End Effects of Wing Tips
Tip vortex created by flow from high-pressure side to low-pressure side of wing.
Tip vortices from heavy aircraft far downstream and pose danger to light aircraft.

34. Lift Generated by Spinning
Superposition of Uniform stream + Doublet + Vortex

35. Drag Coefficient: CD Stokes’ Flow, Re<1 Supercritical flow
turbulent B.L.
Relatively constant CD

36. Drag
Drag Coefficient
with or

37. Friction has two effects:
DRAG FORCE
Friction has two effects:
Skin friction due to shear stress at wall
Pressure drag due to flow separation
Total drag due to
viscous effects
Called Profile Drag
Drag due to
skin friction
Drag due to
separation = +
Less for laminar
More for turbulent
More for laminar
Less for turbulent

38. COMPARISON OF DRAG FORCES
Same total drag as airfoil

39. AOA = 2°

40. AOA = 3°

41. AOA = 6°

42. AOA = 9°

43. AOA = 12°

44. AOA = 20°

45. AOA = 60°

46. AOA = 90°

47. Drag Coefficient of Blunt and Streamlined Bodies
Drag dominated by viscous drag, the body is __________.
Drag dominated by pressure drag, the body is _______.
streamlined
bluff
Flat plate

48. Drag Pure Friction Drag: Flat Plate Parallel to the Flow
Pure Pressure Drag: Flat Plate Perpendicular to the Flow
Friction and Pressure Drag: Flow over a Sphere and Cylinder
Streamlining

49. Drag Flow over a Flat Plate Parallel to the Flow: Friction Drag
Boundary Layer can be 100% laminar, partly laminar and partly turbulent, or essentially 100% turbulent; hence several different drag coefficients are available

50. Drag Flow over a Flat Plate Perpendicular to the Flow: Pressure Drag
Drag coefficients are usually obtained empirically

51. Flow past an object
Character of the steady, viscous flow past a circular cylinder: (a) low Reynolds number flow, (b) moderate Reynolds number flow, (c) large Reynolds number flow.

52. Drag
Flow over a Sphere and Cylinder: Friction and Pressure Drag (Continued)

53. Streamlining
Used to Reduce Wake and hence Pressure Drag

54. Lift
Mostly applies to Airfoils
Note: Based on planform area Ap

55. Lift
Induced Drag

56. Experiments for Airfoil Lift & Drag
Examine the surface pressure distribution and wake velocity profile on airfoil 2-D
Compute the lift and drag forces acting on the airfoil
Pressure coefficient
Lift coefficient

57. Airfoil Temp. sensor Pitot tubes Pressure sensors Data acquisition
Test Facility:
Wind tunnel.
Airfoil
Temp. sensor
Pitot tubes
Pressure sensors
Data acquisition

58. Test Design Airfoil in a wind tunnel with
free- stream velocity of 15 m/s.
This airfoil has:
Forces normal to free stream = Lift
Forces parallel to free stream = Drag
Top of Airfoil:
- The velocity of the flow is greater
than the free-stream.
- The pressure is negative
Underside of Airfoil:
- Velocity of the flow is less than the
free-stream.
- The pressure is positive
This pressure distribution contribute
to the lift & Drag

59. Pressure taps positions

60. measured pressure distribution over the Airfoil’s surface.
The lift force, L on the Airfoil will be find by integration of the
measured pressure distribution over the Airfoil’s surface.

61. Data reduction
Calculation of lift force
The lift force L= Integration of the measured pressure over the airfoil’s surface.
Pressure coefficient Cp where, pi = surface pressure measured, = P pressure in the free-stream
U∞ = free-stream velocity,
ϱ = air density
pstagnation = stagnation pressure
by pitot tube,
L = Lift force, b = airfoil span,
c = airfoil chord

62. Drag Force
The drag force, D on the Airfoil = Integration of the momentum loss using the axial velocity profile in the wake of the Airfoil.

63. Data reduction The drag force D = integration of the momentum loss
Calculation of drag force
The drag force D = integration of the momentum loss
The velocity profile u(y) is measured ui at predefined locations
U∞ = free-stream velocity,
ϱ = air density
pstagnation = Stagnation pressure
by Pitot tube,
D = Drag force, b = airfoil span,
c = airfoil chord

64. Velocity and Drag: Spheres
General relationship for submerged objects
Spheres only have one shape and orientation!
Where Cd is a function of Re

65. Sphere Terminal Fall Velocity

66. Sphere Terminal Fall Velocity (continued)
General equation for falling objects
Relationship valid for spheres

67. Drag Coefficient on a Sphere
1000
100
Stokes Law
Drag Coefficient 10 1
0.1
0.1 1 10
102
103
104
105
106
107
Re=500000
Reynolds Number
Turbulent Boundary Layer

68. Drag Coefficient for a Sphere: Terminal Velocity Equations
Valid for laminar and turbulent
Laminar flow R < 1
Transitional flow 1 < R < 104
Fully turbulent flow R > 104

69. Example Calculation of Terminal Velocity
Determine the terminal settling velocity of a cryptosporidium oocyst having a diameter of 4 mm and a density of 1.04 g/cm3 in water at 15°C.
Reynolds