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Chapter 10

Fluids

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Units of Chapter 10

Phases of Matter

Density and Specific Gravity

Pressure in Fluids

Atmospheric Pressure and Gauge PressurePascals Principle

Measurement of Pressure! Gauges and the

"arometer

"uoyancy and Archimedes Principle

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10,1 Phases of Matter

(he three common phases of matter are solid)

li&uid) and gas-

A solid has a definite shapeand si.e-

A li&uid has a fi/ed volume*ut can *e any

shape-

A gas can *e any shape and also can *e easily

compressed-

i&uids and gases *oth flo#) and are called

fluids-

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10, Density and Specific Gravity

(he density2lower case Greek rho)of an o*3ect

is its massper unit volume'

(he S+ unit for density is 4g5m6

- Density is alsosometimes given in g5cm6! to convert g5cm6to

4g5m6) multiply *y 1000-

7ater at 89C has a density of 1 g5cm6: 1000 4g5m6-

(he specific gravityof a su*stance is the ratio of

its density to that of #ater-

SG = (/water) = 10-3

210,1;

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10,6 Pressure in Fluids

Pressureis defined as the forceper unit area-

Pressure is a scalar! the units of pressure in the

S+ system are pascals'

1 Pa = 1 N/m2

Pressure is the same in every

directionin a fluid at a given

depth! if it #ere not) the fluid#ould flo#-

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Also for a fluid at rest) there is nocomponent of force parallelto any

solid surface < once again) if there

#ere the fluid #ould flo#-

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(he pressureat a depth h*elo# the surface of

the li&uid is due to the #eightof the li&uid a*oveit- 7e can &uic4ly calculate'

(his relation is valid for any li&uid #hose density

does not change #ith depth-

At rest Fy= 0

F - mg = 0 F = mgF = mg = Vg, V =Ah

F = Ahg

P F/A = gh

Pressure at depth h(fluid at rest)

P = gh

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Section 10-4: Atmospheric Pressure

Earths atmosphere:A fluid.

But doesnt have a fixed top surface! Change in height habove Earths surface

Change in pressure P =gh

ea levelPA 1.013 105N/m2

= 101.3 kPa

1 atm

"ld units 1 bar = 1.00 105N/m2

Physics:auseof pressure at an# height

$eight of air above that height!

This pressure des !t crushus" as ur ce##s mai!tai! a! i!ter!a#

pressure that ba#a!ces it.

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$h% ip

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10,8 Atmospheric Pressure and Gauge

Pressure

Most pressure gaugesmeasure the pressure

a*ovethe atmospheric pressure < this is called

the gauge pressure-

(he a*solute pressureis the sum of the

atmospheric pressure and the gauge pressure-

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Conceptual %/ample 10,8

P = ?

Pressure onA:

Pdown= P + Pmg

Pup= PA

At restFy= 0

Pup= Pdown

or PA = P + Pmg

P = PA - Pmg < PA

So, air pressure holds

fluid in straw!

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10,= Pascals Principle

+f an e/ternalpressure is applied to a confined

fluid) the pressure at everypoint #ithin the fluidincreases *y that amount-

(his principle is used) for e/ample) in hydraulic

liftsand hydraulic *ra4es-

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10,> Measurement of Pressure! Gauges and

the "arometer

(here are a num*er of different types ofpressure gauges %&ost useP ' PA= gh =

P( =gauge pressure'- (his one is an open,

tu*e manometer- (he pressure in the

open end is atmosphericpressure! the

pressure *eing measured #ill causethe fluid to riseuntil

the pressures on *othsides at the same

height are e&ual-

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the "arometer

?ere are t#o more devices formeasuring pressure' the

aneroid gaugeand the tire

pressure gauge-

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!arious Pressure "nits

(auge )ressureP(= gh

A#ter!ate u!it ) pressure:*nstead ofcalculatinggh+ co,,on to use standard li-uid

%,ercur#+ g or alcohol+ /hereis standard'0 ,easure h

#uote pressure in $en%th units! 1or exa,ple,illi,eters of ,ercur#

mm *g

1or h =1 mm *g = 10'3m *g

&mercur'%h = (13

104

*%/m3

) (+, m/s

)(10-3

m)= 133 ./m = 133 Pa

1 orr

%another pressure unit!'

mm *g &Trrare not proper * pressure units!

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the "arometer

(his is a mercury*arometer)developed *y (orricelli to measure

atmospheric pressure- (he height

of the column of mercuryis such

that the pressure in the tu*e at the

surface level is

1 am-

(herefore) pressure is often

&uoted in millimeters2or inches;

of mercury-

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the "arometer

Any li&uid can serve in a(orricelli,style *arometer)

*ut the most denseones

are the most convenient-

(his *arometer uses #ater-

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Pro*- 1@'(A variation on Exaple "#$)

2an3 depth = 5 m

)ipe length = 110 m

ill slope = 5+,

(auge )ressureP(= ?

eight /ater*shoots

fro, bro3en pipe at

botto,4

eight of /ater level in

tan3 fro, house level h = -5 110 si!5+, = +.3 mP( =%atergh = -110

3 kg/m3-.+ m/s2-+.3 m = .

105N/m2

Conservation of energ#* = h = +.3 m%5eglects frictional effects+ etc.'

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10,@ "uoyancy and Archimedes Principle

(his is an o*3ect su*mergedin a fluid- (here is a

net forceon the o*3ect *ecause the pressures atthe top and *ottom of it are different-

(he *uoyant forceis

found to *e the up#ard

force on the samevolume

of #ater'

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Archimees Princip$e

2he total %up/ard' buo#ant force on an o2ectof

volu,e 4co,pletel# or partiall# sub,erged in a $ui /ith

densit#

=4g (1)

4 m &ass of fluid /hich /ould ta3e up sa,e

volu,e as ob6ect+ if ob6ect /ere not there. %&ass of fluid

that used to be /here ob6ect is!'

p%ard buya!t )rce

= mg ()

= /eight of fluid displaced b# the ob6ect!

-1or -2

Archimedes Pri!cip#e

)roved for c#linder. Can sho/ valid for an# shape

10 " d A hi d P i i l

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(he net force onthe o*3ect is then the difference

*et#een the *uoyant forceand the gravitationalforce-

10 @ " d A hi d P i i l

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+f the o*3ects densityis lessthan that of #ater)

there #ill *e an up#ardnet force on it) and it #illrise until it is partially outof the #ater-

10 @ " d A hi d P i i l

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For a floatingo*3ect) the fraction that is

su*mergedis given *y the ratio of the o*3ectsdensityto that of the fluid-

F

o

o

disp

VV

=

10 @ " d A hi d P i i l

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(his principle also #or4s in

the air! this is #hy hot,airand

helium*alloons rise-

789:8;:

'8;:%

ecall the $or3?Energ# )rinciple

!et = @ = -B -B

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-B-722 ' -B-712= P1' P2' g-y2> y1 (4)

>e/rite (4)as

P1 -B-712 gy1 = P2 -B-722 gy2

er!u##iCs @Duati!

Another for,P -B72 gy= c!sta!t

5ot a ne/ la/+ 6ust /or3 0 energ# of s#ste, in fluid

language. %Nte#P g-y2'y1since fluid isNETat rest!'

9or* one ' Pressure= @ P@

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6$ow on the $e;e$

P1 -B-712 gy1 = P2 -B-722 gy2

1lo/ on the level y1 = y2

P1 -B-712= P2 -B-722

Explains ,an# fluid pheno,ena 0 is a

-uantitative state,ent ofer!u##iCs Pri!cip#e:

Fhere the )#uid 7e#city is high" the

pressure is #%" a!d %here the 7e#city is#%" the pressure is high.G

10 10 Applications of "ernoullis

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10,10 Applications of "ernoullis

Principle' from (orricelli to Airplanes)

"ase*alls) and (+A

Using "ernoullis principle) #e find that the speed

of fluid coming from a spigoton an opentan4 is'

(his is called

(orricellistheorem-

210,>;

P1 -B-712 gy1 = P2 -B-722 gy2

P1 = P2

P2

P1

10 10 Applications of "ernoullis Principle'

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10,10 Applications of "ernoulli s Principle'

ifton an airplane #ingis due to the different

air speedsand pressureson the t#o surfaces

of the #ing-

PTEPH PET

IJT )rceKA1Area of /ing top+A2Area of /ing botto,

TEP = PTEPA1 ET = PETA2

)lane /ill fl# if L = ET ' TEP '

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10,10 Applications of "ernoulli s


"ase*alls) and (+A

A *alls path #ill curvedue to its

spin) #hich results in the air

speeds on the t#o sides of the

*all not *eing e&ual-


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"ase*alls) and (+A

A person #ith constricted

arteries #ill find that they

may e/perience a

temporary lac4 of *lood tothe *rain 2(+A! (ransient

+schemic Attac4; as *lood

speeds up to get past the

constriction) there*y

reducingthe pressure-


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"ase*alls) and (+A

A venturi metercan *e used to measure fluid

flo#*y measuring pressuredifferences-

10,10 Applications of "ernoullis

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"ase*alls) and (+A

Air flo#across the top helps smo4e go up a

chimney) and air flo# over multiple openings can

provide the needed circulationin underground

*urro#s-

P *l 8> P i t

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Pro*lem 8>' Pumping #ater up

$treet level# y1= 0

71= 0. m/s" P1= 3.+ atm

%iameter d1= 5.0 cm

(r1= 2.5 cm A1= -r12

' m up# y2= 1+ m"d2= 2. cm(r2= 1.3 cmA2= -r2

2

72= 8 P2= 8

)ontinuit"#A171= A272 72= -A171/-A2 = 2.22 m/s

Bernoulli#

P1 -B-712 gy1= P2 -B-72

2 gy2

P2= 2.0 atm

Summary of Chapter 10

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Phases of matter' solid) li&uid) gas-

i&uids and gases are called fluids-

Density is mass per unit volume-

Specific gravity is the ratio of the density of the

material to that of #ater-

Pressure is force per unit area-

Pressure at a depth hisgh-

%/ternal pressure applied to a confined fluid is

transmitted throughout the fluid-


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Atmospheric pressure is measured #ith a

*arometer-

Gauge pressure is the total pressure minus the

atmospheric pressure-

An o*3ect su*merged partly or #holly in a fluidis *uoyed up *y a force e&ual to the #eight of

the fluid it displaces-

Fluid flo# can *e laminar or tur*ulent-

(he product of the cross,sectional area and the

speed is constant for hori.ontal flo#-


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7here the velocity of a fluid is high) the

pressure is lo#) and vice versa-

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