Chapter 10: Fluid Mechanics
Objectives:
 Define:
 Relative and absolute motion
 Buoyancy
 Pressure
 Fluid
 Drag force
 Lift force
 Explain how a fluid exerts forces on an object moving through it
 Identify the components of fluid forces
 Distinguish between surface drag and form drag
 Describe Bernoulli's Principle
 Describe the Magnus effect
 Identify the various factors that determine the effect fluid forces have on an object
Can humans fly?
Fluid: A liquid or gas
Buoyant force: Upward force acting on an object in a fluid that is equal to the weight of the fluid displaced by the object
Dunking a ball in the water: What determines a buoyant force?
Buoyant force is equal to the weight of the fluid displaced.
Density of an object will determine whether an object will float or not.
ρ = m/V
ρ = density
m = mass
V = volume

What affects motion through a fluid?
Surface  Shape  Size  Velocity  Density
Drag Force: The component of dynamic fluid force that acts in opposition to the relative motion of the object with respect to the fluid.
Surface Drag: Drag force acting on an object within a fluid and caused by friction between the fluid and the surface of the object.
Form Drag: Drag force acting on an object within a fluid and caused by the impact forces of the fluid molecules with the object.
Drag Force: F_{D} = ½C_{D}ρAv^{2}
Bob Beamon's Long Jump Record (Relative and absolute motion)
How was each factor from the drag force equation modified in Bob Beamon's jump?
Drag Forces in Sport
Speed Skiing,
Cycling,

 Drafting behind one rider = 27% reduction in VO_{2}
 Drafting behind two in front, 3 in next row = 39% reduction in VO_{2}
 Drafting behind vehicle = 62% reduction in VO_{2}
From Lukes RA et al. (2005) The understanding and development of cycling aerodynamics, Sports Engineering, 8, 5974.
Greg Lemond vs (video)

Running
Should grown men shave their legs?
Calculating drag in speed skiing
Drag Force on a Speed Skier:
Drag Coefficient ~ 0.7
Frontal Area ~ 0.5 m^{2}
Density ~ 1 kg/m^{3}
Speed ~ 50 m/s
F_{D} = 438 N
What keeps skiers
from going faster ?

Terminal velocity: The ultimate speed that can be attained when falling under the influence of gravity (skydiving)
Terminal Velocity balances
Gravity vs Drag Force:
F_{gravity} = F_{drag}
m g sin θ = (0.5) C_{D} A ρ V^{2}
How fast is terminal velocity ?
Terminal Velocity of Speed Skier:
Drag Coefficient ~ 0.7
Frontal Area ~ 0.5 m^{2}
Density ~ 1 kg/m^{3}
Slope ~ 45 degrees
Mass ~ 70 kg
V = 52.6 m/s if g = 9.8 m/s^{2}


What happens with larger mass ?
Current world record: Simone Origone 156mph


Textbook example
Lift Force
Bernoulli's Principle: Fastermoving fluids exert less pressure laterally that do slowermoving fluids.
F_{L} = ½C_{L} A ρ v^{2}
Magnus Force (Tennis Ball Backspin)
Curveball
Fluid forces in swimming
Swimsuit effect on performance
SwimSport online magazine, April 2000

Example of how fluid forces affect motion of projectiles
Gravity and air density variations
Air density is based upon:
 Air pressure
 Temperature
 Humidity
