1. Dynamic Fluid Forces Forces that result when an object moves through a fluid, or when a fluid moves past an object. Pages 197-210 in book

2. Dynamic Fluid Force Arises due to the relative motion of an object in a fluid. There must be motion!! F  ½C D  Av 2 C D = Drag coefficient  = Fluid density A = Surface area perpendicular to flow v = Relative velocity of object and fluid

3. Water Skiing ViVi Water Particle VfVf Two things happen to the particle of water when it comes in contact with the ski. 1.It’s direction will change 2.It’s speed will be reduced This means the particle underwent acceleration, which means forces must have been acting on the particle.

4. The Force on the Water Particle ViVi VfVf VV  V = V f - V i F = ma Acceleration is change in velocity over time F = m (  V/  t) The force must act in the same direction as the acceleration vector, and the acceleration vector must act in the same direction as the change in velocity vector determined above. F

5. The Force on the Ski (Dynamic Fluid Force) Newton’s 3 rd Law: for every force there is an equal and opposite force We’ve determined the force of the ski on the water, therefore we now know the force of the water on the ski. F This force can be broken down into components that act perpendicular and parallel to the direction of motion. Lift: Always perpendicular to motion. Not necessarily in the up direction. Drag : Always parallel to motion.

6. Drag Force Surface Drag: Viscous drag, or skin friction Form Drag: Shape, profile, or pressure drag

7. Surface Drag Boundary Layer: Layer of fluid that clings to and moves with the object. This layer produces an external force on the object. The boundary layer has an external force acting on it from the adjacent layer of fluid. This process eventually dissipates. The roughness of the surface and how long the air molecules are in contact are large influences on surface drag.

8. Form Drag Form drag is influenced by the shape and the size of the object. In particularly, it is influenced by the cross-sectional area of the object that is perpendicular to the relative motion. Air Molecules Big deflection means a big force must have caused the change in direction.

9. Form Drag The relative shape of the object to the direction of motion affects the movement of the air molecules. A large blocking shape results in large changes to the direction of the air molecules. The larger the change in direction, the larger the force required. This means large reaction force back on the object.

10. Form Drag and Fluid Flow Air molecules hitting the leading surface increase form drag Air molecules hitting the trailing surface reduce from drag, because they have components directed towards the front of the object. The type of fluid flow determines whether air molecules hit the trailing surface. Laminar: Molecules remain close to surface of object Turbulent: Molecules deflected away from object and therefore do not hit the trailing end of the object.

11. TURBULENT FLOW

12. LAMINAR FLOW

14. BASEBALL LAMINAR FLOW

15. GOLF BALL LAMINAR FLOW Better than baseball

16. TENNIS BALL : MORE TURBULENT

17. No Spin: New Fuzzy Ball No Spin: Old Smoother Ball

18. Tennis Ball Hit with Top Spin Direction of Flight Final path of air

19. Tennis Ball Hit with Back Spin Direction of Flight Final path of air

20. Trade Off Between Surface Drag and Form Drag? Check out Spoiler aerodynamics webpage in Favorites

24. Flow Visualization Of Wake Asymmetry on Spinning Golf Ball