Download L 15 Fluids [4] Bernoulli`s principle WIND

Basic principles of fluid motion
I. Continuity equation:
v × A = constant Æ v1A1 = v2A2
L 15 Fluids [4]
> Fluid flow and Bernoulli’
Bernoulli’s principle
> Airplanes and curveballs
> viscosity
> surface tension
v1
A1
A2
v2
II. Bernoulli’s principle states that as the
speed of a moving fluid increases, the
pressure within the fluid decreases.
Bernoulli’s principle
• fast flow Æ low pressure
• slow flow Æ high pressure
Low
pressure
High
pressure
Blowing air over the top of the tube lowers the
air pressure on that side allowing the fluid to rise
No flow
Why does a roof blow off in high
winds ?
Low Pressure
Flow on top
Wind tunnel visualization of air flow
streamlines
WIND
Normal
Pressure
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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
pressure
Bernoulli’s Principle
ƒ Fluid flow velocity = v
ƒ Fluid pressure = P
Æ where v is high, P is low
Æ where v is low, P is high
Low
pressure
Frames of reference
• The jet moves
through the air
Streamlines around a wing
• From the perspective of
the jet, the air moves
relative to the jet
wing
Flow over an airplane wing
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
Curveballs
High speed,
Low P
Banked turn
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.
Airflow around a baseball that is NOT spinning
• The ball is moving but
from the ball’s
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
Curveballs & Screwballs
the lift on a rotating
body moving through
a fluid is called the
MAGNUS FORCE
low speed,
high P
Viscosity
• so far we have considered
only “ideal” liquids Æ 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
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.
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.
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?
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 Î it does flow, but
very slowly!
• viscosity depends on temperature Î
warm syrup flows faster than cold syrup
Measuring viscosity
ball
bearings
viscosity indexhot engine
viscosity indexcold engine
A higher viscosity index indicates the viscosity
changes less with temperature than a lower viscosity index.
low viscosity
Liquid (e. g. water)
Flow through a pipe
P1
P2
high viscosity
Liquid (e.g. syrup)
Blood flow in arteries
D
L
volume flow rate ∝
( P2 − P1 ) i D 4
L iη
big
effect!
η (eta) is the fluid’s viscosity
A pipe clogged
With calcium
deposits
• A 10 % reduction in diameter reduces the flow by 34 %
• If D Æ D/2, the flow is reduced by 94 %
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SURFACE TENSION
Suspended by 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
soap films
measuring surface tension forces
soap film
W
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