The Physics of Fluids High School Teachers Workshop American Physics Society, Division of Fluid Dyna

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The Physics of FluidsHigh School Teachers
WorkshopAmerican Physics Society, Division of
Fluid DynamicsSaturday, November 22, 2008San
Antonio, Texas
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Agenda

• Introductions 900-915
• The Physics of Fluids 915-950
• Important Properties
• Fluid Forces
• Governing Principles
• Description of experiment
• Break
• Water Gun Experiment 1000-1100
• Break
• Flow Visualization 1110-1150
• Wrap-up

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Workshop Instructors

• Professor Karen Flack
• Department of Mechanical Engineering
• United States Naval Academy, Annapolis, Maryland
• Professor Doug Bohl
• Department of Mechanical and Aeronautical
  Engineering
• Clarkson University, Potsdam, New York
• Professor Bud Homsy
• Department of Mechanical Engineering
• University of California, Santa Barbara

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Fluid Mechanics

• Hydrostatics stationery fluid
• Forces on dams, piers, etc.
• Fluid Dynamics moving fluid
• Pipe flow
• Pumps, turbines
• Flow over shapes (ship hulls, automobiles, wings,
  etc)
• Lift and Drag

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Important Properties

• Pressure
• Density
• Viscosity

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Important Property - Pressure

• Static Pressure
• P? g H
• Dynamic Pressure
• P1/2?V2

Pbottom (?gH)orange (?gH)red(?gH)green
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Important Properties - Density

• Density (?) Mass/Volume

Weight m g
?mercury 13,600 kg/m3 ?water 1000
kg/m3 ?air 1.23 kg/m3
Buoyant Force (? Vol)disp g
Density Rainbow
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Important Properties - Viscosity

• Viscosity
• Resistance to shearing motion
• Stickiness

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Fluid Forces

• Body Forces
• Normal Forces
• Shear Forces
• Surface Tension

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Fluid Forces

• Body Forces

Weight m g
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Fluid Forces
F m g

• Normal Force
• Pressure x Area

F P A
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Fluid Forces

• Surface Force shear stress x Area

F t A
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Fluid Forces

• Surface Force shear stress x Area

F t A
Definition of a fluid Deforms continuously with
shearing
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Fluid Forces

• Surface Tension - Imbalance of cohesive forces

Imbalance of cohesive forces
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Governing Principals

• Conservation of Mass
• Conservation of Momentum
• Conservation of Energy
• Generation of Entropy

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Conservation of Mass

• Mass in Mass out Mass stored

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Conservation of Mass

• Mass in Mass out Mass stored

Un-steady Problem Mass in 0 Mass out
(?AV)outmout Mass stored dm/dt ? fluid
density A cross sectional area V fluid
velocity t time
.
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Conservation of Mass

• Mass in Mass out Mass stored

Steady Problem Mass flow in (?AV)in min Mass
stored 0 Mass flow out (?AV)out mout ?
fluid density A cross sectional area V fluid
velocity For incompressible (?const) (AV)in
(AV)out able to solve for V
.
.
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Conservation of MomentumNewtons 2nd Law

• Momentum in forces on an object
• momentum out stored momentum

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Conservation of MomentumNewtons 2nd Law
Lift
Thrust
Drag
Weight
Thrust
.
(mV)out
.
(mV)in
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Conservation of MomentumNewtons 2nd Law
Fanchor
PinA
.
.
(mV)in
(mV)out
.
.
mout min (conservation of mass) (?AV)out
(?AV)in ? constant (incompressible) Aout lt
Ain Vout gt Vin
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Conservation of MomentumNewtons 2nd Law
Fanchor
PinA
.
.
(mV)in
(mV)out
.
.
mout min (conservation of mass) (?AV)out
(?AV)in ? constant (incompressible) Aout lt
Ain Vout gt Vin
Firefighter has to hold on tight!
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Conservation of Energy

• Energy in energy generated energy out
• stored energy

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Conservation of Energy

• Energy in energy generated energy out
• stored energy

Flow work F x (P A) x P (A x)P Vol m P
Vol/m m P/? Potential Energy m g z Kinetic
Energy ½ m V2 Mechanical Energy ? pump,
turbine, etc. Electrical Energy Heat Lost
Energy ? friction!
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Conservation of Energy

• Heat in Kinetic Energy in Work in
• Work out Kinetic Energy out Lost Energy

Heat in
Kinetic energy in
Kinetic energy out lost energy
Work out
Work in
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Conservation of Energy

• Potential Energy in Electrical Energy out
  Lost Energy

Potential energy in

Electrical energy out lost energy
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Generation of Entropy

• Entropy is a measure of disorder
• Processes occur in a direction such that entropy
  is always created
• Entropy in entropy out gt 0

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Water Gun Experiment

• Banzai Aquazone
• Water Blaster

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Water Gun Experiment

• How many pumps of a
• water gun does it take
• to hit a target at a
• known distance?

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Water Gun Experiment

• Principles covered
• Ballistics
• Conservation of Energy
• Bernoulli
• Ideal gas law
• Conservation of Mass

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Water Gun Experiment

• Supplies needed
• At least two water guns
• one for firing
• one for taking measurements
• Volumetric cylinder
• Ruler
• Tape measure

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Water Gun Experiment

• Ballistics
• Equations of motion (constant acceleration)
• z final vertical position
• zo initial vertical position
• Vo initial vertical velocity 0
• t time of flight (initial time is t 0)
• ao initial vertical acceleration gravity
  -9.81 m/s2

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Water Gun Experiment

• Ballistics (cont)
• Solve for time of flight
• The nozzle velocity, VN, necessary for a
  specified horizontal distance, ?x, can be
  determined (neglecting drag on the fluid stream)

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Water Gun Experiment

• Conservation of Energy
• Energy in Energy out Lost energy
• Flow work P? mP?/m mP/? (? volume)
• Kinetic energy ½ mV2 (V velocity)
• Potential Energy mgz
• Lost energy friction
• in tank (T), out nozzle (N)

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Water Gun Experiment

• Neglecting frictional losses and dividing by
  mass, the
• conservation of energy equation is reduced to
  Bernoulli.
• This equation will be used to solve for the tank
  pressure (PT)
• Assuming VT 0, ?T ?N (incompressible
  water), zT zN

PN Patm 101,000 Pa 101 kPa
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Water Gun Experiment

• Ideal Gas Law
• The ideal gas constant is used to determine the
• volume of air in the tank for a required tank
  pressure.
• For R and T constant
• Solve for the final (pumped up) air density, ?f,
  for
• Pi Patm, Pf PT and ?i ?air at Troom

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Water Gun Experiment

• Conservation of Mass
• massin massout stored mass
• During the pumping process massout 0
• massfinal massinitial massin
• The initial mass of air is determined from the
  ideal gas law
• The mass if air pumped into the tank, min, is
  determined from
• the final density, ?f

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Water Gun Experiment

• Conservation of Mass
• The volume or air added is now determined
• The number of pumps required (N) is the
  determined
• by the volume of air needed and the volume for
  each
• pump, ?p
• where di and L are the inner diameter and length
  of the
• cylindrical bore.

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Water Gun Experiment

• Perform calculations for a known distance (?x),
  final height (z), and initial height (zo).
• Students should fire the water gun using
  calculated number of pumps (N).
• The water should fall short of the distance due
  to the fact that the calculations did not account
  for frictional losses in the gun and drag on the
  fluid stream.

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Water Gun Experiment

• Lets do the lab!

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Water Gun Experiment

• Accounting for frictional losses Conservation
  of Energy

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Water Gun Experiment

• Accounting for frictional losses Conservation
  of Energy

In terms of in tank and out nozzle, as
defined previously
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Water Gun Experiment

• Accounting for frictional losses Conservation
  of Energy

In terms of in tank and out nozzle, as
defined previously
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Water Gun Experiment

• Calculate actual nozzle exit velocity

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Water Gun Experiment
Define Losses loss of kinetic energy based on
VN Losses ½ K?VN2 K loss
coefficient
Solve for K and PT
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Water Gun Experiment

• Solve for new number of pumps using the ideal gas
  law and
• conservation of mass

Fire again!
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Water Gun Experiment

• What worked?
• Areas for improvement?
• Ideas for implementation