Summary … Fluids - Nevis Laboratoriessciulli/Physics1401/lectures/Lecture19disp.pdfPhysics 1401 -...
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slide 1 Physics 1401 - L 19 Frank Sciulli Summary … Fluids l Density ( r ), pressure (p) , … l Pressure transmitted uniformly and isotropically (all directions): Paschal’s Principle l Pressure vs depth for static liquid l Bouyancy: upward force = weight of displaced liquid (Archimedes) l Fluids in motion for ideal fluids (laminar, incompressible, nonviscous, …) l Equation of continuity ( r vA=constant) l Work-energy requirement ( p+ r v 2 /2 + r gy = constant): Bernouli’s equation l Implications (more today) And then Chapt. 19 … Temperature, Heat, and the beginnings of Thermodynamics
Transcript of Summary … Fluids - Nevis Laboratoriessciulli/Physics1401/lectures/Lecture19disp.pdfPhysics 1401 -...
slide 1Physics 1401 - L 19 Frank Sciulli
Summary … Fluidsl Density (ρ), pressure (p), …l Pressure transmitted uniformly and isotropically (all
directions): Paschal’s Principlel Pressure vs depth for static liquidl Bouyancy: upward force = weight of displaced liquid
(Archimedes)l Fluids in motion for ideal fluids (laminar, incompressible,
nonviscous, …)l Equation of continuity (ρvA=constant)l Work-energy requirement (p + ρv2/2 + ρgy = constant):
Bernouli’s equationl Implications (more today)
And then Chapt. 19 … Temperature, Heat, and the beginnings of Thermodynamics
slide 2Physics 1401 - L 19 Frank Sciulli
Hydrodynamic Relations
l Venturi tube demo
l Air flow demo
Equation of ContinuityAv Av=1 1 2 2
Bernouli's Equationp v gy p v gyρ ρ ρ ρ+ + = + +2 21 1
1 1 1 2 2 22 2
A Av vp p
<><
2 1
2 1
2 1
review
slide 3Physics 1401 - L 19 Frank Sciulli
Sample Problem 15-9
Find velocity of water when it exits tank
2 21 11 1 1 2 2 22 2p v gy p v gyρ ρ ρ ρ+ + = + +
210 0 2
Top of tank <=> Hole in tank0 0
2
p gh p v
v gh
ρ ρ+ + = + +
=Note same v as if it were
dropped from height hSame pressure - Cons Energy
slide 4Physics 1401 - L 19 Frank Sciulli
Viscosity and geometry limit utility of Bernouli’s equation
Bernouli's Equationp v gy p v gyρ ρ ρ ρ+ + = + +2 21 1
1 1 1 2 2 22 2
l Viscosity measures friction between fluid and pipe, nozzle,
l Vertical nozzle: doesn’t quite rise to ideal heightu Clearly oil (more viscosity) rises
even lessl But Bernouli explains a lot: …l Pix shows real case for water
and nozzle
? 2v gh
slide 5Physics 1401 - L 19 Frank Sciulli
How airplane wings lift
ab
a’b’
l Potential energies ( y ) difference negligible
l Streamline flow requires time to travel a-> a’ be the same as time for b -> b’
l For a the distance traveled is larger, so velocity must be higher (va>vb)
l From Bernouli’sequation: pa< pb
2 21 11 1 1 2 2 22 2p v gy p v gyρ ρ ρ ρ+ + = + +
( )( )
a ab b
ab
p p v vF p p A
ρ− = −
= −
2 212
slide 6Physics 1401 - L 19 Frank Sciulli
House Plumbing
l Why have “elbow” or “trap”? …u needs water in trap to work properly (acceptably) u Having only air between B and A produces smelly bathrooms –
due to the main sewer linel Plumbing in left figure doesn’t work:
u water in trap gets sucked out when large volume of water flows at A to main sewer (eg, someone upstream showers) so that pressure at A lowered
l Plumbing in right figure works: u the way real house plumbing is done
slide 7Physics 1401 - L 19 Frank Sciulli
1 2
Blood Flow in Arteries
l Plaque buildup in artery (arteriosclerosis) means (eqn of continuity) speed in blockage higher than in unblocked artery
l Speed higher in blockage means pressure is lower there (Bernouli eqn)
l Lower pressure makes artery more likely to collapse
2 1
2 1
2 1
A Av vp p
<><
Note opposite happens when artery inflates = embolism
1 1 2 2
2 21 11 1 1 2 2 22 2
Av Av
p v gy p v gyρ ρ ρ ρ
=
+ + = + +
slide 8Physics 1401 - L 19 Frank Sciulli
Throwing Curves
2
1
l Left: no spin, thrown ball flies straightl Right: ball spins (cc-wise)
u Viscosity makes air flow faster around side 2 than side 1u Bernouli’s eqn: p2 < p1u Net force (side 2 – side 1) produces “curve ball”u Also works for “drop ball” …
2 21 11 1 1 2 2 22 2p v gy p v gyρ ρ ρ ρ+ + = + +
2 1
2 1
v vp p
><
ω
slide 9Physics 1401 - L 19 Frank Sciulli
Heat and Temperature topics (begins in Chapter 19)
l Temperature vs Heatl Measuring temperaturel Temperature scales and absolute zerol Thermal expansionl Heat capacity (absorption)u Specific heatu phase transitions
l Heat and Workl 1st law of thermodynamicsl heat transfer
today
slide 10Physics 1401 - L 19 Frank Sciulli
Heat and Temperaturel Rely initially on your intuitive sense +
u temperature is a property of a body reflecting our sense of “hot” and “cold”
u heat is a form of energyl Intuition: a body with high temperature has more
“heat” than it would have at low temperaturel Temperature initially measured empirically to
conform to this intutitionl Bodies at the same temperature are in thermal
equilibriuml Thermal equilibrium – bodies in contact ultimately
come to the same temperature
• 19th century brought under-standing that temperature is a measure of the average random speed of molecules
slide 11Physics 1401 - L 19 Frank Sciulli
Joule’s Experimentl 1843 – James Prescott Joule showed that a specific amount of
mechanical energy reproducibly raised the temperature of a material
l Demonstrated that lost mechanical energy (in closed system) can be accounted as Heat: u the “Conservation of Total Energy” = First Law of Thermodynamics
l 1 calorie = 4.186 J raises 1 gram of water from 14.5oC to 15.5oC
Q C TQ cm T
≡ ∆≡ ∆
C = heat capacity
c = specific heatWill return to this
slide 12Physics 1401 - L 19 Frank Sciulli
Heat energy moves
l Heat energy (Q ) always flows from hot body to cold bodyu aside: we will consider this later as a statement, or
consequence, of the Second Law of Thermodynamicsl Like other forms of energy (kinetic, potential, …)
Q is measured in Joulesu also calories, BTU, ... Read text!
l In upper and lower illustration to left, the system and environment u Will initially exchange heat energyu Then rate of exchange will slow down as
temperatures get closeru Both systems will ultimately arrive at the same
temperature, and then Q=0 (as in middle figure)l Now we have two laws of thermodynamicsl First discuss ways of measuring temperature and
effects of temperature on materials
slide 13Physics 1401 - L 19 Frank Sciulli
Familiar Temperature Measuresl Rely on (for now)
empirical factuMost materials expand
when temperature increases
l Old fashioned glass thermometer, with bulb and capillary containing fluidu If temperature increases,
fluid expands into capillary
u Scale provides measure
Large volume bulb filled with fluid
Capillary where fluid expands to
slide 14Physics 1401 - L 19 Frank Sciulli
l Fixed amount of gas and fixed volume of bulb
l ~1800: find empirically pressure and temperature proportional to each other
l Will return to this and other “ideal gas laws” later
Gas Thermometer
Gay-Lussac LawT p∝
slide 15Physics 1401 - L 19 Frank Sciulli
oC oF K
Temperature Scales set with Water (freeze and boil)
l Define temperature scales l Gas thermometer can measure
temperature of bath by extrapolating p (or V) of gas to zero
o
o
95 32
273 15.CF
C K
T TT T
= +
= −
freezingwater
slide 16Physics 1401 - L 19 Frank Sciulli
Gas Thermometer and Absolute Zero
l Measure temperature and pressure over range where it remains a gasu Most cases, a phase change will occur
l find empirically pressure and temperature proportional to each other (Gay-Lussac)
T Cp=
l extrapolate to lower temperaturesl all gases: extrapolation intercepts
p=0 at T0=-273.15oC = absolute zero
slide 17Physics 1401 - L 19 Frank Sciulli
Real Temperatures and Lifel Temperature (we now know and will soon demonstrate) is a measure
of the average random motion (kinetic energy) of moleculesl No temperature can be lower than absolute zerol Absolute zero is where all molecular motion stops
lifelife
slide 18Physics 1401 - L 19 Frank Sciulli
Temperature Scales and Expansion
L L Tα∆ = ∆
l Three temperature scales l Mass of any system stays
constant (until Relativitistic Quant Mech)
l Empirically as temperature increases, most materials increase their volume
l Coefficient of linear expansion, α (small)u Typically ~10-6 to 10-3 (0C)-1
slide 19Physics 1401 - L 19 Frank Sciulli
Area and Volume Changes
How much do circle, hole, and ruler change in area?
( )( )( ) ( )( )( )
x x x x
x y
A A TA A L L L L
L T L TA T
A A T
γ
α α
α
α
γ α
∆ ≡ ∆
+ ∆ = + ∆ + ∆
= + ∆ + ∆
≈ + ∆
∆ = ∆
=
1 11 22
2
How much do solids change in volume?
3V V Tβ
β α
∆ ≡ ∆
=
Temperature increase causes most material volumes to increase = density decrease
slide 20Physics 1401 - L 19 Frank Sciulli
Use Material Expansion for Thermometers
l See table for typical expansionsl Note: fluid in “mercury thermometer” expands
more than the glass envelopeu Liquids typically expand more than solidsu Gases (fixed pressure) typically expand more than
liquidsl Different gases have similar values … see later
slide 21Physics 1401 - L 19 Frank Sciulli
Insight into Expansion with TemperatureMolecular explanation:
u as temperature of solid increases, molecules move faster around average locations, but further from each other (expansion)
u High enough temp (kinetic energy), bonds holding atoms in lattice break (liquid), but forces still hold atoms nearby (not fixed average location like solid) and more temp makes for greater separations (expansion)
u Raise temp even higher, bonds completely break --- gas ---more temp, more energy (expansion)
l PHASE CHANGES
Solid Liquid Gas
slide 22Physics 1401 - L 19 Frank Sciulli
Heat and Temperature
Remember to leave HW8 in box
------------------So Far
l Temperature vs Heatl Measuring
temperaturel Temperature scales
and absolute zerol Thermal expansion
To Comel Heat capacity (absorption)
uSpecific heatl phase transitionsl Heat and Workl Develop 1st law of
thermodynamicsl heat transfer
u conductionu convectionu radiation
l Kinetic Theory of Gases
