☰ Chapter 10: Fluid Mechanics

• 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?
Photo by Jonathan Francis on Unsplash

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. \(ρ = {m \over V} \) \(ρ = density\) \(m = mass\) \(V = volume\)

What affects motion through a fluid?

Surface - Shape - Size - Velocity - Density

Drag Force: A 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 surface of the object and the fluid.
Form Drag: Drag force acting on an object within a fluid caused by the difference in pressure between two sides of the object.

Drag Force: \( F_D = {1 \over 2} C_D A ρ v^2 \)

Bob Beamon in Flight: Mexico City Olympics 1968 World Record 8.90 meters Unknown - [1] Dutch National Archives, The Hague, Fotocollectie Algemeen Nederlands Persbureau (ANEFO), 1945-1989 bekijk toegang 2.24.01.04 Bestanddeelnummer 922-2039 CC BY-SA 3.0 Selected Track & Field Results from the 1968 Olympic Games

Vale93b CC BY-SA 3.0

Murray Foubister CC BY-SA 2.0

Drafting behind one rider = 27% reduction in VO2 Drafting behind two in front, 3 in next row = 39% reduction in VO2 Drafting behind vehicle = 62% reduction in VO2 From Lukes RA et al. (2005) The understanding and development of cycling aerodynamics, Sports Engineering, 8, 59-74. Greg Lemond prior to the 1989 Tour de France final time trial (behind by 50 seconds) Greg rode the 15.2 mile race 58 seconds faster than Lauren Fignon to win the Tour de France. He average 33.9 mph.

Calculating drag in speed skiing

Drag Force on a Speed Skier: Drag Coefficient ~ 0.7 Frontal Area ~ 0.5 m2 Density ~ 1 kg/m3 Speed ~ 50 m/s  FD = 438 N What keeps skiers from going faster ?

Terminal Velocity \(F_{gravity} = F_{drag} \) \(-mg sinθ = {1 \over 2} C_D A ρ v^2 \) \( v = \sqrt{{-2mg sinθ} \over {C_D ρ A}} \) How fast is terminal velocity ? Terminal Velocity of Speed Skier: Drag Coefficient ~ 0.7 Frontal Area ~ 0.5 m2 Density ~ 1 kg/m3 Slope ~ 45 degrees Mass ~ 70 kg V = 52.6 m/s if g = -9.8 m/s2 What happens with larger mass ? Current world record: Simone Origone 156mph

Skier simulation

\( F_L = {1 \over 2} C_L A ρ v^2 \)



Magnus Force (Tennis Ball Backspin)

Curveball

Fluid forces in swimming
Swimsuit effect on performance

2009 US Swim Trials

Example of how fluid forces affect motion of projectiles
Gravity and air density variations

Air density is based upon:

• Air pressure
• Temperature
• Humidity