Fluid Mechanics

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Fluid Mechanics
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Today.

• Understand the ways in which flow affects fluid
  forces
• Explore buoyancy and its variables
• Define lift and drag and their effect on movement

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Introduction

• Why do golf balls have dimples?
• Why can some people float and other cannot?
• Why do some athletes try to streamline their
  bodies during competition?

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A little golf ball history

• Original golf balls were smooth
• Nicks and cuts from use
• turbulators
• Created turbulent boundary layer
• Reduces drag

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Flow

• Caused by object moving through fluid
• Laminar flow characterized by smooth parallel
  layers of fluid
• Turbulent flow layers of fluid near the surface
  of the object mix
• If turbulence is present flow is non-laminar
• speed related properties
• Effect of surface area

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The nature of fluids

• Are all fluids liquids?
• Fluids all liquids and gases.
• Water is a fluid and a liquid. Air is a fluid and
  a gas.
• Liquid tends always to occupy the same volume
• Gas changes volume by expanding or contracting to
  fill or fit into any container
• substance that tends to flow deform when acted
  on by a shear force
• Air and water act on the body

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Relative motion

• Influence of fluid depends on velocity of body
  velocity of fluid
• Relative velocity velocity of body w/respect to
  the velocity of the surrounding fluid

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Relative velocity

• If motion is opposite fluid flow the magnitude of
  the velocity of the body is the sum of the speeds
  of the body and the fluid
• If motion is in the same direction as the fluid,
  the magnitude of the bodys velocity is the
  difference in the speeds

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Relative velocity
Cyclist velocity 15 m/s
Velocity of cyclist Relative to wind 20 m/s
Cyclist velocity 15 m/s
Velocity of cyclist Relative to wind 10 m/s
Wind velocity ? 5 m/s
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Other fluid properties

• Density ? mass/volume
• Specific weight ? weight/volume
• Viscosity resistance to flow
• All affected by atmospheric pressure
  temperature

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Buoyancy

• Archimedes principle buoyant force is equal to
  the weight of the fluid displaced by the body
• Fb Vd?

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Buoyancy

• Example water polo ball with a volume of 0.2m3
  is completely submerged in 20C water, the
  buoyant force acting on the ball is equal to the
  balls volume X the specific weight of water at
  that temp
• Fb (0.2m3)(9790N/m3)
• Fb 1958 N

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Buoyancy

• gtdensity of fluid, gt magnitude of buoyant force
• Buoyant force acts on center of volume

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Flotation

• Related to body density
• Two people w/identical volume
• One weighs more (higher density)
• Volume must be large enough to create Fb gt body
  weight

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Flotation

• Relationship between center of volume and center
  of gravity

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A look at airplanes
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airplanes.

• Thrust Drag
• Lift Weight
• If drag gt thrust, the plane will slow down
• If thrust and is gt drag, the plane will speed
  up.
• if lift drops lt the weight of the airplane, the
  plane will descend.

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Thrust

• force that must be created to overcome the drag
• thrust propellers, jet engines, kicking

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Drag

• force that resists the motion of an object moving
  through a fluid
• Hand our car window example
• Factors affecting drag
• drag increases velocity
• Skiing example
• Landing gear

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Drag

• Skin friction, surface drag, viscous drag
• ..derived from friction between adjacent layers
  of fluid near a body moving through the fluid..
• Factors
• Relative velocity of fluid flow
• Surface area of the body
• Roughness of surface
• Viscosity of fluid

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Drag

• Form drag, profile drag, pressure drag
• resistance created by a pressure differential
  between the lead and rear sides of a body moving
  through a fluid..
• Factors
• Velocity of body
• Pressure gradient between front rear ends of
  body
• Size of surface area perpendicular to flow

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Drag

• Wave drag
• ..resistance created by the generation of waves
  at the interface between two different fluids..

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Wonder about 747s?
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Lift

• force that holds airplane in the air
• created primarily by wings
• exist in presence of moving fluid
• relative difference in speeds between the object
  and the fluid
• Object moving/fluid stationary
• Object still/fluid moving

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How is lift created?

• force on a wing in a moving fluid
• acts perpendicular to the flow of the fluid
• Drag same thing, but parallel to the direction
  of the fluid flow

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How is lift created?

• A compressed into the air above it as it moves
  upward
• B slowed, compressed and redirected in a
  downward path
• C lift component
• D net force
• E drag

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Lift force

• Factors
• Velocity of foil relative to fluid
• Fluid density
• Surface area of the flat side
• Angle of attack

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Magnus effect/force

• spinning object traveling through liquid is
  forced to move sideways
• Curve ball example
• spinning action on release
• spinning causes air to flow differently
• top of the ball vs under the ball
• top of the ball is spinning directly into air and
  the bottom of the ball is spinning with the air
  flow
• air under the ball is flowing faster than air on
  top
• creates less pressure, forces the ball to move
  down or curve.

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Magnus force

• Spinning objects generate lift
• Effect trajectory deviation toward the direction
  of spin