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## Balls in Flight and Fluid Dynamics Chapter 11

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**1. **1 Balls in Flight and Fluid DynamicsChapter 11

**2. **2

**3. **3 Recall: Fluid =
Air is a

**4. **4 Viscosity The ability of a fluid to provide resistance against objects moving through it
Defined as:
? = coefficient of dynamic viscosity
t = shear stress
(dv/dy) = rate of shear
Given in Pa.s

**5. **5 Viscosity cont’d Shear stress:
Objects sliding past each other creating friction
Shear force divided by area over which it acts

**6. **6 Viscosity Causes an irreversible loss of energy
Viscosity of water: 0.001 Pa.s

**7. **7 Forces on an object in a fluid environment Buoyant forces:
Attributable to an object’s immersion in fluid
Act vertically upward
Dynamic forces:
Attributable to an object’s relative motion in fluid
Resolved in drag and lift forces

**8. **8 Cube in water -- FBD Forces
Weight of cube
Water pressure on sides
Upper force
Weight of water above cube
Buoyant force
Weight of volume of fluid displaced by the object

**9. **9 Buoyancy Forces cont’d
The size of buoyant force is equal to the weight of volume of fluid displaced by object.

**10. **10 Density and Specific Gravity Density is:
Given in kg/m3
V = volume
m = mass

**11. **11 Density and Specific Gravity cont’d Density of water:
1000 kg/m3
Density of air:
1.2 kg/m3
Dependent on temperature and pressure

**12. **12 Density and Specific Gravity cont’d Specific gravity:
Ratio of weight of an object to weight of an equal volume of water
Objects with SG < 1 will float

**13. **13 Buoyancy of the Body Lean tissues have densities greater than 1000kg/m3.
Fat/air densities less than 1000 kg/m3
Basis for hydrostatic weighing

**14. **14 Note: location of Fb depends on varying densities in body. A moment arm can result.

**15. **15 Dynamic Fluid Forces Dynamic fluid forces proportional to:
Density of fluid
Surface area of object
Square of velocity of object WRT fluid

**16. **16 Dynamic Fluid Forces cont’d Drag force:
CD = drag coefficient

**17. **17 Relative Velocity
Difference between object’s velocity and fluid’s velocity

**18. **18 Drag Force Component of dynamic fluid force
Acts in opposition to relative motion of object with respect to fluid

**19. **19 Drag Force cont’d Two types of drag
Surface drag
Form drag

**20. **20 Surface Drag Molecules slide past the surface and decelerate
This also slows down nearby molecules
Sum of friction forces

**21. **21 Form Drag A fluid molecule bounces off the surface and is then pushed back toward it by other molecules
Sum of impact forces

**22. **22 Lift Force Acts perpendicular to relative motion of object with respect to fluid
CL = coefficient of lift
FL = lift force

**23. **23 Bernoulli’s Principle Faster-moving fluids exert less pressure laterally than slower-moving fluids
Example: airfoil

**24. **24 Spin and Magnus Effect Magnus effect:
lift forces occur when balls are spinning
Backspin
Topspin
Sidespin

**25. **25 Boundary Layer Narrow layer of viscous air lying over object as it travels through the air
Reynold’s number describes flow conditions around an object

**26. **26 Boundary Layer cont’d Reynold’s number
r = radius of ball
v = velocity
? = density of air
? = viscosity of air

**27. **27 Boundary Layer cont’d Flow conditions can be:
Laminar (Re < 500)
Turbular (Re > 500)

**28. **28

**29. **29 Seams and stitches Disrupt boundary layer flow

**30. **30 Less drag? Instability in the boundary layer allows faster moving air to mix with the slow moving air near the surface
Allows air to flow farther around the ball before the boundary layer separates
Smaller turbulent wake, reduced drag