Flowing fluids

1
Flowing fluids
The OMG chapter Airplane flight
Curveballs And other hopeless nightmares to
explain
A frightening glimpse at the real world
Thomasina Mountains are not pyramids, trees are
not cones.
2
Show phases app website

• Fluids move
• Individual atoms/molecules move
• But so do currents in liquids winds in gases
• These can be described in simple cases, but
• Sometimes it gets really messy (hurricanes, etc)
• And no one knows how to solve the messy problems.

3
Bernoullis principal principle

• What is the energy of a moving cube of water?

Change the height of the cube costs energy
(force) ? (distance) mgh r ? (volume) ? gh
Change the horizontal position costs energy
(force) ? (distance) P ? (area) ? (width) P
? (volume)
While the fluid moves at speed v, it has kinetic
energy (1/2) mv2 (1/2) ? r ? (volume) ? v2
constant
energy density (energy/volume) rgh P
(1/2)rv2
4
The Bernoulli principle, Jr

• Be careful It only applies along
• streamlines, which
• Follow little volumes of fluid
• Most calculations done when
• streamlines are smooth,
• or even parallel

But in many real situations theres
turbulence and the bed time stories are not good
descriptions
5
Streamlines turbulence

• Rising incense smoke will be
• laminar for a while in a still room

But inevitably a small wiggle appears and starts
to grow
And then all heck breaks loose and there is
turbulence or chaos
There are no simple equations that we can write
for the tangled mess so we make up big
words like turbulence
6
What do I do now??

• How do I know if it is turbulent?
• In calculations for PHYS100,
• its never turbulent.
• Always use Bernoulli equation.
• What about in the real world?
• If the fluid moves slowly, its probably not
  turbulent
• If the fluid is very viscous, its probably not
  turbulent

7
What is this good for?

• rgh P (1/2)rv2 constant
• How do we know
• there is no turbulence?
• We just hope it is a small effect
• so we assume that Bernoulli
• gets the essence right.

8
Firefighting

• What is the pressure drop as water goes into a 3
  cm diameter nozzle from a 9 cm diameter fire hose
  at a flow of 40 L/s?
• How high can this water rise go into the air?

9
Silly demo tools

• Blow along the top of a strip
• of paper
• It rises up towards the air stream
• Bernoulli sez
• high speed air makes
• lower pressure on top of the strip, so it
  floats up.
• It flaps around crazily because the airstream is
  turbulent

10
Why those darn trucks make your car swerve

• Air squeezed between vehicles
• flows faster and pressure
• drops
• If you are passing you tend
• to drift towards the truck
• Usually frowned upon unless
• corrected for immediately

(If you drive close behind you feel/hear
turbulence)
11
Slow as molasses in winter

• Viscosity is resistance to flow
• Results from friction among fluid atoms
• Dramatically slows fluid near a solid surface (v
  ? 0).
• Representative values (water 1.0 centi-Poise)

12
Crazy units for viscosity

• From xtronics.com/reference/viscosity.htm
• Probably because no one could pronounce his name,
  Poiseuille became a hard working student. Like
  many of the French, he had a name that is
  impossible to pronounce or spell. To start with
  imagine you are all puckered up, ready to kiss,
  just as your partner stomps painfully on your
  toe. The sound that comes out is "Poise".
  Phonetically it is spelled pwaz.  (Hint Be sure
  to practice in a place where you won't
  accidentally spit on someone.) All that is left
  is uille.  A big help when pronouncing French
  words is to ignore the sounds of the all the
  letters.  The syllable uille has no U, I, L, or E
  sound.  Fill your mouth full with peanut butter,
  plug your nose, and say sores. Phonetically it
  is a little like zuhrz.

13
If you dont believe in viscosity

• Try drinking honey through a straw
• Or squeezing ketchup through a straw
• Or waiting for the sap to drain in February
• Or flying in an airplane
• Or hitting a good pitchers breaking stuff

14
The Koufax miracle

• I can understand how he won 25. What I can't
  understand is how he lost five."-- Yogi Berra

Led NL in E.R.A. 5 years in a row Lifetime 0.95
ERA in 4 World Series 4 no-hitters (one perfect
game) 3 Cy Young awards (NLAL) 11 shutouts in
1963
15
The magicians wrist

• Snaps the wrist to spin the ball with
• forward rotation
• Viscous drag of ball on the air makes
• air move slower on top and
• faster on the bottom.

Bernoulli says that Ptop lt Pbottom So ball is
pushed down by the pressure difference
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You thought floating a boat was entertaining

• Basically the same effect in wings
• caused by curved surfaces
• instead of by rotation.
• Air going under the wing is crowded
• and moves slower
• Air going above is rarefied
• and moves faster
• So there is net upward force

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Take home messages

• Buoyant force is weight of displaced fluid
• Gas is compressible liquid is not
• Pressure increases with depth P rgh
• Bernoulli Principle rgh P (1/2)rv2
  constant