1. 17. Drag
CH EN 374: Fluid Mechanics

2. Drag is the force a flowing fluid exerts on a body.

3. 𝑭 𝑫 = 𝝉 𝒘 𝑨 Drag comes entirely from viscous shear stress
This is friction drag

4. 𝑭 𝑫 =𝚫𝐏𝑨 No shear stress here—where does drag come from?
This is form drag (or pressure drag)

5. Flow Separation Wakes form when flow separates behind an object
They are low pressure and usually turbulent

6. What kind of drag explains why a marble drops more slowly through syrup than vegetable oil?

7. Δ𝑃 is usually much larger than 𝜏 𝑤
So which kind of drag is usually more significant?
Do you think friction drag is more likely to be significant in laminar flow or turbulent?

8. Lift
𝑭 𝑳
𝑭 𝑫
𝑭 𝑷
Lift is the component of pressure and shear forces around a body that are normal to flow.

9. Angle of Attack
Airplane wings (for example) are designed with a shape and angle of attack to maximize lift and minimize drag.

10. Why do airplane wings have those retractable flaps?

11. Streamlining

12. Is there any particular reason to streamline an iron?

13. Which of these cars experiences more friction drag?
So why does streamlining decrease drag?

14. Flow Separation and Streamlining
Streamlining mitigates flow separation.
A non-streamline shape is also called a “bluff” body

15. 𝐶 𝐷 = 𝐹 𝐷 𝐴 1 2 𝜌 𝑣 2 Drag Coefficient
𝐶 𝐷 = 𝐹 𝐷 𝐴 𝜌 𝑣 2
Where A is the projected area of the object.

16. 𝐶 𝐷 = 2 𝐹 𝐷 𝜌 𝑣 2 𝐴 Drag Coefficient
𝐶 𝐷 = 2 𝐹 𝐷 𝜌 𝑣 2 𝐴
Where A is the projected area of the object.

17. 𝐹 𝐷 = 1 2 𝐶 𝐷 𝜌 𝑣 2 𝐴 Drag Coefficient
𝐹 𝐷 = 1 2 𝐶 𝐷 𝜌 𝑣 2 𝐴
Where A is the projected area of the object.

18. Frontal Area Example 𝒗 𝐴= 𝒗 𝐴=

19. Terminal Velocity 𝑣 𝑡𝑒𝑟𝑚 = 2𝑊 𝐶 𝐷 𝜌𝐴 𝑭 𝑫 𝑾
A falling object will stop accelerating when:
𝑭 𝑫 𝑾
𝐹 𝐷 =𝑊
𝐹 𝐷 = 1 2 𝐶 𝐷 𝜌 𝑣 2 𝐴→𝑊= 1 2 𝐶 𝐷 𝜌 𝑣 𝑡𝑒𝑟𝑚 2 𝐴
𝑣 𝑡𝑒𝑟𝑚 = 2𝑊 𝐶 𝐷 𝜌𝐴

20. How does a parachute work?
How does a parachute decrease terminal velocity?
𝑣 𝑡𝑒𝑟𝑚 = 2𝑊 𝐶 𝐷 𝜌𝐴

21. Car Evolution

22. Finding Drag Coefficient
𝐶 𝐷 for most shapes can be assumed constant after 𝑅𝑒≈ 10 4
Discuss why you think the 𝐶 𝐷 curve changes with Re.