L 15 Fluids [4]

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L 15 Fluids 4

• gt Fluid flow and Bernoullis principle
• gt Airplanes and curveballs
• gt viscosity
• gt surface tension

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Basic principles of fluid motion

• I. Continuity equationv ? A constant ? v1A1
  v2A2
• II. Bernoullis principle states that as the
  speed of a moving fluid increases, the pressure
  within the fluid decreases.

v1
3
Blowing air over the top of the tube lowers
the air pressure on that side allowing the fluid
to rise
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Bernoullis principle

• fast flow ? low pressure
• slow flow ? high pressure

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Why does a roof blow off in high winds ?
WIND
Low Pressure
Normal Pressure
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Wind tunnel visualization of air flow
streamlines
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Streamlines and fluid flow

• The black lines are the paths that the fluid
  takes as it flows.
• Wider spacing indicates low speed flow, narrow
  spacing indicates high speed flow
• Color indicates pressure

High
Low pressure
pressure
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Bernoullis Principle

• Fluid flow velocity v
• Fluid pressure P
• ? where v is high, P is low
• ? where v is low, P is high

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Frames of reference

• From the perspective of the jet, the air moves
  relative to the jet

• The jet moves through the air

10
Streamlines around a wing
11
Flow over an airplane wing
12
Control surfaces on a plane

• By extending the slats, the wing area can be
  increased to generate more lift at low speeds for
  takeoff and landing

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How does a plane turn?
Lift Force
Level Flight
Banked turn
14
Airflow around a baseball that is NOT spinning

• The ball is moving but from the balls
  perspective the air moves relative to the ball
• The streamlines are bunched at the top and bottom
  indicating higher flow speed
• The pressure forces are balanced

15
Curveballs
The ball is rotating clockwise. The layer of air
adjacent to the ball is dragged along by the
rotation, causing the flow speed to be higher on
the top side. The higher pressure on the
bottom causes the ball to curve upward.
High speed, Low P
the lift on a rotating body moving through a
fluid is called the MAGNUS FORCE
low speed, high P
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Curveballs Screwballs
the dimples on a golf ball are there to increase
the air drag on the rotating ball (back spin)
causing it to experience extra lift.
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Viscosity

• so far we have considered only ideal liquids ?
  liquids that can flow without any resistance to
  the flow
• real liquids (like ketchup) have a property
  called viscosity which is a tendency for the
  liquid to resist flowing

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viscosity

• for example pancake syrup flows more slowly
  than water we say that pancake syrup is more
  viscous than water.
• Ketchup and molasses are also good examples
• viscosity is sometimes referred to as the
  thickness of a liquid
• viscosity is the most important property of motor
  oil

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Seeing the effects of viscosity
Pancake syrup
Substances with higher viscosity take longer
to flow down the ramp.
viscosity is a measure of the resistance that
one layer of liquid experiences when flowing over
another layer.
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Viscosities of various substances

• water has a viscosity of about 1 unit
• pancake syrup has a viscosity of 2500
• ketchup has a viscosity of 98,000
• Lava- 100,000
• peanut butter has a viscosity of 250,000
• glass is a liquid with a very high viscosity of
  1017 ? it does flow, but very slowly!
• viscosity depends on temperature ? warm syrup
  flows faster than cold syrup

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Motor Oil

• SAE Society of American Engineers
• the viscosity of oil tends to decrease as it
  heats up (oil breakdown)
• what does 10W-30 mean?

viscosity index- hot engine
viscosity index- cold engine
A higher viscosity index indicates the viscosity
changes less with temperature than a lower
viscosity index.
22
Measuring viscosity
ball bearings
low viscosity Liquid (e. g. water)
high viscosity Liquid (e.g. syrup)
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Flow through a pipe
big effect!
? (eta) is the fluids viscosity

• A 10 reduction in diameter reduces the flow
  by 34
• If D ? D/2, the flow is reduced by 94

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Blood flow in arteries
A pipe clogged With calcium deposits
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SURFACE TENSION
a surface tension force causes a fluid surface to
behave like an elastic sheet
Molecules at the surface feel a net force
insect on water surface
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Suspended by surface tension
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soap films
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measuring surface tension forces