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