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Chapter Chapter 1010
FluidsFluids
PhasesPhases
SolidSolid Liquid Liquid
GasGas
Fluids Fluids Plasma Plasma DensitDensity
p “rho”p “rho” p = m/v SI Units Kg/mp = m/v SI Units Kg/m33
Sometimes g/ cmSometimes g/ cm33
1 kg/m1 kg/m33 = .001 g/cm = .001 g/cm33
Ex: Al p= 2.7 g/cmEx: Al p= 2.7 g/cm33
=2700 kg/m=2700 kg/m33
specific gravity – the ratio of the specific gravity – the ratio of the density of that substance to the density of that substance to the density of water at 4density of water at 4°°CC
SG No UnitsSG No Units The SG of any substance will be The SG of any substance will be
equal numerically to its density in equal numerically to its density in g/cmg/cm33 or 10 or 10-3-3 times its density in times its density in kg/mkg/m33
continued…continued…
SG SG Pb= 11.3Pb= 11.3 Alcohol = .79Alcohol = .79 Al= 2.7Al= 2.7
SG will tell you if substance floats SG will tell you if substance floats or notor not
>1 sink <1 >1 sink <1 FloatFloat
Atmospheric PressureAtmospheric Pressure
Pressure due to the Atmosphere, Pressure due to the Atmosphere, changes with depthchanges with depth
Earth’s Atmosphere is complicatedEarth’s Atmosphere is complicated P for air changesP for air changes No distinct top surface to measure hNo distinct top surface to measure h
Atmospheric Pressure is Atmospheric Pressure is 1.013 x 101.013 x 1055 Pa Pa
14.7 psi14.7 psi
10 -3
This is another unit: AtmThis is another unit: Atm 1 atm = 1.013 x 101 atm = 1.013 x 1055 N/m N/m22 (Pa) = 101.3 kPa(Pa) = 101.3 kPa
another unit is the baranother unit is the bar 1 bar= 1 x 101 bar= 1 x 1055 N/m N/m22 1 bar= 100 kPa1 bar= 100 kPa
Gauges measure pressure. Gauges measure pressure. They measure over and above They measure over and above atmospheric pressure. To get atmospheric pressure. To get absolute pressure, one must absolute pressure, one must add atmospheric pressure to add atmospheric pressure to gauge pressure.gauge pressure.
P= PP= Patmatm + P + PGG
ExampleExample
car tire gauge reads 220 kPa, car tire gauge reads 220 kPa, Absolute pressure within the tire Absolute pressure within the tire is 220 kPa + 101 kPais 220 kPa + 101 kPa
=321 kPa=321 kPa
33 psi + 14.7 psi = 47.7 psi33 psi + 14.7 psi = 47.7 psi
Pressure
P= f/A Force/ Area P= f/A Force/ Area Force applied to area Force applied to area
SI unit is N/mSI unit is N/m22 Pascal, Pa Pascal, Pa 1 Pa = 1 N/m1 Pa = 1 N/m22 PSI? PSI?
FeetFeet
psipsi
Fluids exert a pressure equal Fluids exert a pressure equal in all directionsin all directions
*overhead picture**overhead picture*car tire, swimming poolcar tire, swimming pool
In fluids, force always acts In fluids, force always acts to the surfaceto the surface
as depth increases within a as depth increases within a fluid, so does pressurefluid, so does pressure
FormulasFormulas
P= f/AP= f/A
f= mg =maf= mg =ma
m= pvm= pv
m=pAhm=pAh
P=pA hgP=pA hg
AA
P= pghP= pgh
Pressure is directly Pressure is directly proportional to proportional to density density of liquidof liquid and to and to depth depth within liquidwithin liquid
This is This is just for the liquidjust for the liquid- - NOT any external force NOT any external force on the liquidon the liquid
Example Prob.Example Prob.
States that pressure applied to a States that pressure applied to a confined fluid increases the pressure confined fluid increases the pressure throughout by the same amountthroughout by the same amount
Pascal's Principle carries with it Pascal's Principle carries with it hydraulics (pg. 280)hydraulics (pg. 280)
Changing the Area changes the force Changing the Area changes the force For this to be true, the fluid must not For this to be true, the fluid must not
compress (effectively they don’t) compress (effectively they don’t)
Blaise Pascal, French 1623 - Blaise Pascal, French 1623 - 16621662
PPinin = P = Pout out Input Output Input Output
FFoutout F Finin
AAoutout A Ainin
FFinin= F= Foutout(A(Ainin))
AAoutout
A small force can be used to A small force can be used to exert a larger force by making exert a larger force by making the area of one piston larger the area of one piston larger than the area of anotherthan the area of another
Small input area, Large output Small input area, Large output area greatly multiplies the area greatly multiplies the input forceinput force
F= 200
A= 100
A= 1000
F = 2000in out
FFoutout
FFinin Mechanical Mechanical advantageadvantage
If area is 20x greater then If area is 20x greater then output force will be 20x output force will be 20x greatergreater
MAMA
Homework!Homework!
3 types of buoyancy:3 types of buoyancy:++ rise rise-- sink sinkneutralneutral equilibrium equilibrium
BuoyancyBuoyancy
All objects appear to weigh All objects appear to weigh less when submerged in a fluidless when submerged in a fluid
Why a buoyant force?Why a buoyant force?pg. 283pg. 283
FF22
FF11
FF22> F> F11
FF22 is greater b/c is greater b/c there is more there is more
pressure at the pressure at the lower depthlower depth
This is how we derive the formula…This is how we derive the formula…
FFBB = F = F22 – F – F11
FFBB = Ap = Apf f ghgh22-Ap-Apf f ghgh11
= Ap= Apffg(hg(h22- h- h11))
ApApffgh (Ah = gh (Ah = Vol)Vol)
ppffgVgV
RecallRecall F= APF= AP p= m/vp= m/v w= mgw= mg Vol= AhVol= Ah
Also… pV = mass Also… pV = mass so….so….
mmffg=fg=fBB
Fbuoyant = pfgV= mfg
This is Archimedes Formula This is Archimedes Formula (Principle)(Principle)
In English= In English= The buoyant force on a The buoyant force on a body immersed in a body immersed in a fluid is equal to the fluid is equal to the weight of the fluid weight of the fluid displaced by the objectdisplaced by the object
Lets Test out Archimedes Lets Test out Archimedes Idea and see if he was Idea and see if he was
right…right…1.1. Find m of object ____g weight ___NFind m of object ____g weight ___N2.2. Find V of Object ____cmFind V of Object ____cm33 _____m _____m33
3.3. Find m of submerged ____ g weight ____NFind m of submerged ____ g weight ____N4.4. Find buoyant force on objectFind buoyant force on object
ffBB = weight (air) – weight (submerged) = weight (air) – weight (submerged) = _______ N - _______ N= _______ N - _______ N ffBB= _______N= _______N
Now check w/ formulaNow check w/ formula ffBB= p= pffgVgV = 1 x 10= 1 x 1033 kg/m kg/m33(9.8m/s(9.8m/s22) __________m) __________m33
= ______= ______
% error = 5.7%% error = 5.7%
65.9565.95 .646.646
77 7 x 107 x 10-6-6
58.558.5 .573.573
.646.646 .573.573
7 x 10 7 x 10 - 6- 6
.073.073
.069.069
What about fWhat about fBB = M = Mffgg
Why do steel ships Why do steel ships float?float?
How can fish suspend How can fish suspend themselves in Hthemselves in H2200
How do submarines How do submarines work?work?
Restatement :Restatement : ffBB= W= Wff = p = pff Vg Vg
The volume of an object can The volume of an object can also be found by:also be found by:
VVff= m = w= m = w
ppff gp gp
Archimedes Principle applies to Archimedes Principle applies to both submerged and floating both submerged and floating
objectsobjects
ffBB= weight of object --for floating = weight of object --for floating objectsobjects
ppffVVdispdispg = pg = pooVVoog --g cancelsg --g cancels
VVdispdisp = p = poo
VVoo p pff
Shortcut– sometimes applied (if Shortcut– sometimes applied (if p is known)p is known)
Density of floating object = Density of floating object = fraction of object that density of fraction of object that density of fluid floating in is submerged. fluid floating in is submerged.
wood Logwood Log
waterwater
900 kg/m900 kg/m33
1000 kg/m1000 kg/m33
= .9= .9
9/10 of log 9/10 of log is is
underwaterunderwater
90 % of log is 90 % of log is submergedsubmerged
fluid dynamics (hydrodynamics if fluid dynamics (hydrodynamics if water)water)
If flow is smooth- streamline or If flow is smooth- streamline or LaminarLaminar
if flow is erratic, currents present – if flow is erratic, currents present – turbulentturbulent
Viscosity- internal resistance within Viscosity- internal resistance within fluidfluid
Syrup (high viscosity)Syrup (high viscosity) Water (low viscosity)Water (low viscosity)
Flux- term used to describe Flux- term used to describe Volume of fluid passing through Volume of fluid passing through a given area each seconda given area each second
Rate of Flow - assume ideal Rate of Flow - assume ideal fluid, frictionless, laminarfluid, frictionless, laminar
VelocityVelocity
AreaAreaD= VtD= Vt
flow rate Rflow rate Runitsunits== m m33/s (volume/ /s (volume/
time)time)m/s m/s xx m m22 (m (m33/s)/s)RR== VA Velocity VA Velocity xx
AreaArea
Equation of continuity states Equation of continuity states that rate of flow remains that rate of flow remains constant. Velocity and area constant. Velocity and area will change (inversely), but will change (inversely), but rate (mrate (m33/s) stays the same./s) stays the same.
Area Area 11
Area 2Area 2
Velocity Velocity 11
Velocity 2Velocity 2
because R(mbecause R(m33/t) stays the /t) stays the same…same…
AA11VV11= A= A22VV22
VV11= A= A22VV22
AA11
Large Velocity – Small AreaLarge Velocity – Small Area
Small Velocity- Large AreaSmall Velocity- Large Area
River ExRiver Ex.
FastFast SlowSlow
NarrowNarrowWideWide
Blood Flow Example pg. 288Blood Flow Example pg. 288 Rate of flow of blood in human Rate of flow of blood in human
body stays same –Big Aorta to body stays same –Big Aorta to Small CapillariesSmall Capillaries
Follow along w/ the book to Follow along w/ the book to see how the sample problem is see how the sample problem is solved.solved.
We can also find Power of a We can also find Power of a moving fluidmoving fluid
Power = PRPower = PR Power = pressure x flow ratePower = pressure x flow rate N/mN/m22 x m x m33/s Nm/s J/s/s Nm/s J/s Power = work / timePower = work / time
Where the velocity of a fluid is Where the velocity of a fluid is high, the pressure is low, high, the pressure is low, where the velocity is low, the where the velocity is low, the pressure is high.pressure is high.
1122
V slowV slow
P highP high
V highV high
P lowP low
continued…continued…
This makes sense because This makes sense because if the pressure at 2 were if the pressure at 2 were high it would slow down high it would slow down
the fluid in 1, because the the fluid in 1, because the fluid has sped up, this fluid has sped up, this corresponds to a lower corresponds to a lower
pressurepressure
Want proof?!Want proof?!
Car’s Convertible Top -- jeepCar’s Convertible Top -- jeep Tarp in back of truckTarp in back of truck
carburetor carburetor airplane wingairplane wing
chimneys/ outhouseschimneys/ outhouses perfume atomizerperfume atomizer
Ventilation in burrowsVentilation in burrows hanging ping pong balls hanging ping pong balls ping pong ball = funnelping pong ball = funnel
Here’s the equationHere’s the equation
PP11 + ½ pV + ½ pV1122 + pgy + pgy11 = P = P22 + 1/2pV + 1/2pV22
22 + pgy + pgy22
When solving for PWhen solving for P22 the formula looks the formula looks like this:like this:
PP22 = P = P11 + pg(y + pg(y11-y-y22)+ ½ p(v)+ ½ p(v2211-v-v22
22))
P= pressureP= pressure p= density of flowing fluidp= density of flowing fluid g= gravityg= gravity y= heighty= height V= velocityV= velocity
**Overhead Picture****Overhead Picture**
Bernoulli’s Equation is Bernoulli’s Equation is really an expression of the really an expression of the
law of energy law of energy conservation.conservation.
The formula is derived The formula is derived from work energy from work energy
principle - - pg. 290principle - - pg. 290
Go to overhead for equation…
PP
VelVel
AA
hh