L 15 Fluids  L 15 Fluids 
Basic principles of fluid motion
• Continuity equation:
L 15 Fluids  v × A = constant
A1 A2 v2
>Fluid flow and Bernoulli’s principle
>Airplanes and curveballs • Bernoulli’s principle states that as the
>viscosity (real fluids) speed of a moving fluid increases, the
pressure within the fluid decreases:
P + ½ ρv2 = constant
The Venturi Meter
Blowing air over the top of the tube lowers the
air pressure on that side allowing the fluid to rise
Why does a roof blow off in high
• fast flow low pressure
• slow flow high pressure
No flow Flow on top
Wind tunnel visualization of air flow Streamlines and fluid flow
• The black lines are
the paths that the fluid
takes as it flows.
• Wider spacing
indicated slow speeds
• Color indicates
pressure violet is
high pressure, red is
Bernoulli’s Equation Frames of reference
Fluid flow velocity = u • The jet moves • From the perspective of
the jet, the air moves
Fluid density = ρ (rho) through the air relative to the jet
Fluid pressure = P
Then along a streamline:
P + ½ ρ u2 + ρ g h = constant
where u is high, P is low
where u is low, P is high
Streamlines around a wing Flow over an airplane wing
Control surfaces on a plane How does a plane turn?
• By extending the
slats, the wing area
can be increased
to generate more
lift at low speeds
for takeoff and
Level Flight Banked turn
Airflow around a baseball
Curveballs The ball is rotating clockwise.
that is NOT rotating The layer of air adjacent to the
ball is dragged along by the
• The ball is moving but
rotation, causing the flow speed
from the ball’s
to be higher on the top side. The
perspective the air
High speed, higher pressure on the bottom
moves relative to the ball Low P causes the ball
• The streamlines are to curve upward.
bunched at the top and
bottom indicating higher
• The pressure forces are
Curveballs & Screwballs Viscosity
• so far we have considered
only “ideal” liquids liquids
that can flow without any
• “real” liquids have a property
called viscosity which is a
tendency for the liquid to
viscosity Seeing the effects of viscosity
• for example – pancake syrup flows more Pancake
slowly than water – we say that pancake syrup
Substances with higher
viscosity take longer to
syrup is more “viscous” than water. flow down the ramp.
• Ketchup and molasses are also good
• viscosity is sometimes referred to as the
“thickness” of a liquid
viscosity is a measure of the resistance that one
• viscosity is the most important property of
layer of liquid experiences when flowing over
motor oil another layer.
some viscosity data Motor Oil
• SAE – Society of American Engineers
• water has a viscosity of about 1 unit • the viscosity of oil tends to decrease as it
• pancake syrup has a viscosity of 2500 heats up (oil breakdown)
• ketchup has a viscosity of 98,000 • what does 10W30 mean?
• peanut butter has a viscosity of 250,000
• glass is a liquid with a very high viscosity of viscosity index- meets viscosity viscosity index-
1,000,000,000,000,000 it does flow! cold engine requirements for hot engine
• viscosity depends on temperature, e.g. – winter (low temp)
heating up corn syrup A higher viscosity index indicates the viscosity
changes less with temperature than a lower viscosity index.
Measuring viscosity Flow through a pipe
π i( P2 − P )i D 4
volume flow rate = 1 effect!
η (eta) is the fluid’s viscosity
low viscosity high viscosity • A 10 % reduction in diameter reduces the flow by 34 %
Liquid (e. g. water) Liquid (e.g. syrup) • If D D/2, the flow is reduced by 94 %
a surface tension force
causes a fluid surface to
behave like an
A pipe clogged
deposits Molecules at the surface
feel a net force
insect on water surface
Suspended by surface tension measuring surface tension forces
soap films surface tension effects
Alveoli of the Lungs
The oxygen exchange in the lungs takes place
across the membranes of small balloon-like structures
called alveoli attached to the branches of the bronchial
passages. These alveoli inflate and deflate with inhalation
and exhalation It takes some effort to breathe in because
these tiny balloons must be inflated, but the elastic recoil of
the tiny balloons assists us in the process of exhalation. If the
elastic recoil of the alveoli is compromised, as in the case of
emphysema, then it is difficult to exhale forcibly.
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