The document discusses static fluids and pressure. It defines fluids as substances that lack rigidity and assume the shape of their container. Pressure is defined as the force exerted perpendicularly per unit area. Atmospheric pressure at sea level is approximately 1 atmosphere or 101,325 Pascals. Liquids exert pressure equally in all directions within a container, with pressure increasing with depth and remaining constant horizontally. Pascal's principle states that pressure changes in a confined fluid are transmitted undiminished throughout the fluid.

1. Static FluidsStatic Fluids
• Fluids are substances, such as liquidsFluids are substances, such as liquids
and gases, that have no rigidity. Aand gases, that have no rigidity. A
fluid lacks a fixed shape and assumesfluid lacks a fixed shape and assumes
the shape of its container.the shape of its container.
•In the liquid state, molecules can flow;In the liquid state, molecules can flow;
they freely move from position tothey freely move from position to
position by sliding over one another.position by sliding over one another.

2. PressurePressure
• The pressure P acting on a fluid is the forceThe pressure P acting on a fluid is the force
exerted perpendicularly per unit of theexerted perpendicularly per unit of the
fluid’s surface areafluid’s surface area
• Unit of pressure is the N/mUnit of pressure is the N/m22
or Pascal;or Pascal;
1 N/m1 N/m22
= 1 Pa (Pascal).= 1 Pa (Pascal).
• Atmospheric pressure at sea level isAtmospheric pressure at sea level is
1 atmosphere (atm) = 1.013 x 101 atmosphere (atm) = 1.013 x 1055
Pa.Pa.
• 1 atm = 14.7 lb/in1 atm = 14.7 lb/in22
..
A
F
P =

3. Pressure in a Liquid.Pressure in a Liquid.
• A liquid in a container exerts forcesA liquid in a container exerts forces
against the walls and bottom of theagainst the walls and bottom of the
container.container.
• For a liquid in a container, theFor a liquid in a container, the
pressure the liquid exerts against thepressure the liquid exerts against the
bottom of the container is the weight ofbottom of the container is the weight of
the liquid divided by the area of thethe liquid divided by the area of the
container bottom.container bottom.

4. Measuring PressureMeasuring Pressure
• A manometer is a U-shapedA manometer is a U-shaped
tube that is partially filled withtube that is partially filled with
liquid.liquid.
• Both ends of the tube are openBoth ends of the tube are open
to the atmosphere.to the atmosphere.
• A container of gas is connectedA container of gas is connected
to one end of the U-tube.to one end of the U-tube.
• If there is a pressure differenceIf there is a pressure difference
between the gas and thebetween the gas and the
atmosphere, a force will beatmosphere, a force will be
exerted on the fluid in the U-exerted on the fluid in the U-
tube. This changes thetube. This changes the
equilibrium position of the fluidequilibrium position of the fluid
in the tube.in the tube.

5. AlsoAlso
atmc PP =At point CAt point C
B'B PP =
The pressure at point B is the pressureThe pressure at point B is the pressure
of the gas.of the gas.
PPgaugegauge easily remembered as “hot dog”easily remembered as “hot dog”
'
atm
gauge
B B C
B C B
let d h
P P P h D g
P P P P h D g
P h D g
=
= = + × ×
− = − = × ×
= × ×
From the figure:From the figure:

6. A BarometerA Barometer
The atmosphere pushes on theThe atmosphere pushes on the
container of mercury which forcescontainer of mercury which forces
mercury up the closed, invertedmercury up the closed, inverted
tube. The distance d is called thetube. The distance d is called the
barometric pressurebarometric pressure ..
From the figure:From the figure: atmBA PPP ==
andand
A
let d h
P h D g
=
= × ×
Atmospheric pressure is equivalent to a column of mercuryAtmospheric pressure is equivalent to a column of mercury
76.0 cm tall.76.0 cm tall.

7. DensityDensity
• Density D of a substance is its mass perDensity D of a substance is its mass per
unit volumeunit volume;;
• Objects composed of the same substance,Objects composed of the same substance,
whatever the size or mass, have the samewhatever the size or mass, have the same
density under the same conditions ofdensity under the same conditions of
temperature and pressure.temperature and pressure.
• Temperature and pressure affect theTemperature and pressure affect the
density of substances, appreciably fordensity of substances, appreciably for
gases, but only slightly for liquids andgases, but only slightly for liquids and
solids.solids.
V
M
D =

8. DensityDensity
•How much a liquid weighs and how
much pressure it exerts depends on its
density.
– For the same depth, a denser liquid exerts a
greater pressure than a less dense liquid.
– For liquids of the same density, the
pressure will be greater at the bottom of the
deeper liquid.
• To convert a density in g/cm3
to kg/m3
, multiply
by 1000.

9. Columnar Fluid PressureColumnar Fluid Pressure
(sometimes called gauge pressure)(sometimes called gauge pressure)
• pressure due to apressure due to a
column of fluid of heightcolumn of fluid of height
h and mass density D;h and mass density D;
• The pressure of a liquid atThe pressure of a liquid at
rest depends on therest depends on the
density and depth of thedensity and depth of the
liquid.liquid.
• Liquids are practicallyLiquids are practically
incompressible, so exceptincompressible, so except
for changes in thefor changes in the
temperature, the densitytemperature, the density
of a liquid is normally theof a liquid is normally the
gDhP ⋅⋅=

10. Columnar Fluid PressureColumnar Fluid Pressure
• At a given depth, a given liquidAt a given depth, a given liquid
exerts the same pressure againstexerts the same pressure against
any surface - the bottom or sides ofany surface - the bottom or sides of
its container, or even the surfaceits container, or even the surface
of an object submerged in theof an object submerged in the
liquid to that depth.liquid to that depth.
• Pressure a liquid exerts dependsPressure a liquid exerts depends
only on its density and depth.only on its density and depth.
• Total pressure (or absoluteTotal pressure (or absolute
pressure) Ppressure) Pabsoluteabsolute on a submergedon a submerged
surface equals the pressure thesurface equals the pressure the
liquid exerts plus the atmosphericliquid exerts plus the atmospheric
pressure Ppressure Poo ((1 atm = 1.013 x 101 atm = 1.013 x 1055
Pa)Pa) ..
( )absolute oP P h D g peanut hot dog= + × × +

11. Fluid PressureFluid Pressure
• Pressure of a liquid does notPressure of a liquid does not
depend on the amount of liquid.depend on the amount of liquid.
• Neither the volume or totalNeither the volume or total
weight of the liquid matters.weight of the liquid matters.
• If you sampled water pressureIf you sampled water pressure
at 1 m beneath a large lakeat 1 m beneath a large lake
surface and 1 m beneath asurface and 1 m beneath a
small pool surface, the pressuresmall pool surface, the pressure
would be the same.would be the same.
• The fact that water pressureThe fact that water pressure
depends on depth and not ondepends on depth and not on
volume is illustrated by Pascalvolume is illustrated by Pascal
vases.vases.
• Water surface in each of theWater surface in each of the
connected vases is at the sameconnected vases is at the same
level.level.
• Occurs because the pressures atOccurs because the pressures at
equal depths beneath theequal depths beneath the
surface are the same.surface are the same.

12. FluidFluid
PressurePressure
• At any point within a
liquid, the forces
that produce
pressure are exerted
equally in all
directions.
• Pressure increases
vertically downward.
• Pressure constant
horizontally.

13. Forces Exerted By a FluidForces Exerted By a Fluid
• When the liquid is pressingWhen the liquid is pressing
against a surface there is aagainst a surface there is a
net force directednet force directed
perpendicular to the surface.perpendicular to the surface.
• If there is a hole in theIf there is a hole in the
surface, the liquid initiallysurface, the liquid initially
moves perpendicular to themoves perpendicular to the
surface.surface.
• At greater depths, the netAt greater depths, the net
force is greater and theforce is greater and the
horizontal velocity of thehorizontal velocity of the
escaping liquid is greater.escaping liquid is greater.

14. Transmission of Pressure:Transmission of Pressure:
Pascal’s Principle.Pascal’s Principle.
• Pascal’s Principle: A CHANGEPascal’s Principle: A CHANGE
IN PRESSURE IN A CONFINEDIN PRESSURE IN A CONFINED
FLUID IS TRANSMITTEDFLUID IS TRANSMITTED
WITHOUT CHANGE TO ALLWITHOUT CHANGE TO ALL
POINTS IN THE FLUID.POINTS IN THE FLUID.
• Ex.Ex. Hydraulic lift.Hydraulic lift.
• Hydraulic piston apparatusHydraulic piston apparatus
uses an incompressible fluid touses an incompressible fluid to
transmit pressure from a smalltransmit pressure from a small
cylinder to a large cylinder.cylinder to a large cylinder.
• According to Pascal’s Principle,According to Pascal’s Principle,
the pressure in the smallthe pressure in the small
cylinder resulting from thecylinder resulting from the
application of Fapplication of F11 to ato a
frictionless piston isfrictionless piston is
transmitted undiminished totransmitted undiminished to
the larger piston.the larger piston.

15. Transmission of pressure:Transmission of pressure:
Pascal’s Principle.Pascal’s Principle.
PP11 = P= P22
• AA22 is larger than Ais larger than A11, so the, so the
force exerted by the largeforce exerted by the large
piston is greater than thepiston is greater than the
force exerted on the smallforce exerted on the small
piston.piston.
• AMA (actual mechanicalAMA (actual mechanical
advantage) for hydraulicadvantage) for hydraulic
lift:lift:
2
2
1
1
A
F
A
F
=
1
2
F
F
AMA =

16. Apply a force F1
here to a piston
of cross-sectional
area A1.
The applied force is
transmitted to the
piston of cross-
sectional area A2 here.
F2 = F1
A2
A1

17. Transmission of pressure:Transmission of pressure:
Pascal’s Principle.Pascal’s Principle.
• The figure shows a hydraulicThe figure shows a hydraulic
system used with brakes. Thesystem used with brakes. The
force F is applied perpendicularlyforce F is applied perpendicularly
to the brake pedal. The braketo the brake pedal. The brake
pedal rotates about the axis shownpedal rotates about the axis shown
in the drawing and causes a forcein the drawing and causes a force
to be applied perpendicularly to theto be applied perpendicularly to the
input piston in the master cylinder.input piston in the master cylinder.
The resulting pressure isThe resulting pressure is
transmitted by the brake fluid totransmitted by the brake fluid to
the output plungers which arethe output plungers which are
covered with the brake linings.covered with the brake linings.
The linings are pressed againstThe linings are pressed against
both sides of a disc attached to theboth sides of a disc attached to the
rotating wheel.rotating wheel.

18. BuoyancyBuoyancy
• Buoyancy: the apparent loss ofBuoyancy: the apparent loss of
weight of objects whenweight of objects when
submerged in a liquid.submerged in a liquid.
• Easier to lift objects underEasier to lift objects under
water surface than to lift itwater surface than to lift it
above the water surface.above the water surface.
• When submerged, water exertsWhen submerged, water exerts
an upward force that isan upward force that is
opposite in direction to gravity.opposite in direction to gravity.
Upward force called theUpward force called the
buoyant forcebuoyant force..

19. BuoyancyBuoyancy • Forces exerted by liquidForces exerted by liquid
produce pressure against theproduce pressure against the
submerged object.submerged object.
• Forces are greater at greaterForces are greater at greater
depths; forces are equal atdepths; forces are equal at
the same depth on oppositethe same depth on opposite
sides of the object.sides of the object.
• Forces acting upward on theForces acting upward on the
bottom of the object greaterbottom of the object greater
than those acting downwardthan those acting downward
on top of the object, simplyon top of the object, simply
because the bottom of thebecause the bottom of the
object is deeper.object is deeper.
• Difference in upward andDifference in upward and
downward forces is thedownward forces is the
buoyant force, B.buoyant force, B.
• Fs refers to the force theFs refers to the force the
scale exerts on the mass m.scale exerts on the mass m.
You may also refer to Fs asYou may also refer to Fs as
the tension in a supportingthe tension in a supporting
string.string.

20. BuoyancyBuoyancy
• If the weight of the objectIf the weight of the object
is greater than theis greater than the
buoyant force, the objectbuoyant force, the object
will sink (as in figure a).will sink (as in figure a).
• If the weight of the objectIf the weight of the object
is equal to the buoyantis equal to the buoyant
force, the net force on theforce, the net force on the
object is zero and theobject is zero and the
submerged object willsubmerged object will
remain at any level (as inremain at any level (as in
figure b).figure b).
• If the weight of the objectIf the weight of the object
is less than the buoyantis less than the buoyant
force, the object will riseforce, the object will rise
to the surface and float.to the surface and float.

21. BuoyancyBuoyancy
• When an object is submerged in a liquid, theWhen an object is submerged in a liquid, the
liquid level will rise.liquid level will rise.
• Liquid is displaced or moved elsewhere.Liquid is displaced or moved elsewhere.
• The volume of the liquid displaced is equal toThe volume of the liquid displaced is equal to
the volume of the submerged object.the volume of the submerged object.
• A completely submerged object alwaysA completely submerged object always
displaces a volume of liquid equal to its owndisplaces a volume of liquid equal to its own
volume.volume.

22. Archimede’s PrincipleArchimede’s Principle
• When an object is immersed in a fluid, itWhen an object is immersed in a fluid, it
appears to weigh less.appears to weigh less.
• Archimede’s Principle: THE BUOYANTArchimede’s Principle: THE BUOYANT
FORCE EXERTED ON A BODY WHOLLY ORFORCE EXERTED ON A BODY WHOLLY OR
PARTLY IMMERSED IN A FLUID IS EQUALPARTLY IMMERSED IN A FLUID IS EQUAL
TO THE WEIGHT OF THE FLUIDTO THE WEIGHT OF THE FLUID
DISPLACED BY THE BODY.DISPLACED BY THE BODY.
• Archimede’s Principle applies to bothArchimede’s Principle applies to both
liquids and gases, which are fluids.liquids and gases, which are fluids.
• ImmersedImmersed refers to either completely orrefers to either completely or
partially submerged.partially submerged.

23. Archimede’s PrincipleArchimede’s Principle
• Buoyant force: upward force on the object when it isBuoyant force: upward force on the object when it is
immersed in water.immersed in water.
• The buoyant force (BF) is the weight of the displacedThe buoyant force (BF) is the weight of the displaced
fluid - not the weight of the submerged object.fluid - not the weight of the submerged object.
• BF = (mass in air - mass in fluid)·gBF = (mass in air - mass in fluid)·gravityravity
• BF = weight in air - weight in fluidBF = weight in air - weight in fluid
• BF = weight of displaced fluid (DBF = weight of displaced fluid (Dfluidfluid·V·Vobjectsubmergedobjectsubmerged·g)·g)
• Apparent weight of a submerged object is its weight inApparent weight of a submerged object is its weight in
air minus the buoyant force.air minus the buoyant force.
Apparent weight =Apparent weight = m·g – BF = m·g - Dm·g – BF = m·g - Dfluidfluid·V·Vobject submergedobject submerged·g·g
• For an object that is floating or is submerged but not
sinking: mmobjectobject·g = D·g = Dfluidfluid·V·Vobject submergedobject submerged·g·g

24. FlotationFlotation
• Principle of Flotation: A FLOATINGPrinciple of Flotation: A FLOATING
OBJECT DISPLACES A WEIGHT OFOBJECT DISPLACES A WEIGHT OF
FLUID EQUAL TO ITS OWN WEIGHT.FLUID EQUAL TO ITS OWN WEIGHT.
• A simple relationship between theA simple relationship between the
weight of a submerged object and theweight of a submerged object and the
buoyant force can be found bybuoyant force can be found by
considering their ratio:considering their ratio:
fluidD
objectD
BF
objectFw
=

25. FlotationFlotation
•Shipbuilding and the principle ofShipbuilding and the principle of
flotation:flotation:
– A solid 1-ton block of iron is nearly 8 timesA solid 1-ton block of iron is nearly 8 times
as dense as water, so when it is submerged,as dense as water, so when it is submerged,
it will displace 1/8 ton of water (not anit will displace 1/8 ton of water (not an
amount equal to 8 tons of water).amount equal to 8 tons of water).
– Reshape the iron block into a bowl andReshape the iron block into a bowl and
submerge, displaces a greater volume ofsubmerge, displaces a greater volume of
water. The deeper the bowl is immersed atwater. The deeper the bowl is immersed at
the surface, the more water is displaced andthe surface, the more water is displaced and
the greater is the buoyant force exerted onthe greater is the buoyant force exerted on
the bowl.the bowl.

26. FlotationFlotation
• When the weight of the displaced waterWhen the weight of the displaced water
equals the weight of the bowl - flotation.equals the weight of the bowl - flotation.
Flotation occurs when the weight of theFlotation occurs when the weight of the
bowl equals the buoyant force.bowl equals the buoyant force.
• Every ship must be designed to displace aEvery ship must be designed to displace a
weight of water equal to its own weight.weight of water equal to its own weight.
• Submarines:Submarines:
– Displace a weight of water equal to itsDisplace a weight of water equal to its
own weight, it remains at a constantown weight, it remains at a constant
depth.depth.
– Displaces a weight of water greaterDisplaces a weight of water greater
than its own weight, rises.than its own weight, rises.
– Displaces a weight of water less thanDisplaces a weight of water less than
its own weight, sinks.its own weight, sinks.

27. Buoyancy in Two Liquids ofBuoyancy in Two Liquids of
Differing DensityDiffering Density
• If you have an object submerged in two liquids ofIf you have an object submerged in two liquids of
different density, such that the upper portion ofdifferent density, such that the upper portion of
the object is located in the upper liquid and thethe object is located in the upper liquid and the
lower portion of the object is located in the lowerlower portion of the object is located in the lower
liquid, the total buoyant force on the object isliquid, the total buoyant force on the object is
equal to the weight of the objectequal to the weight of the object
BF = DBF = Dfluidfluid·V·Vobject submergedobject submerged·g·g
• Ex. A piece of wood floating partially in water andEx. A piece of wood floating partially in water and
partially in oil. The density of the oil is less thanpartially in oil. The density of the oil is less than
the density of the water.the density of the water.

28. • Gravity cancels out.Gravity cancels out.
gVDBFBF objectobjectwateroil ⋅⋅=+
gVD)gVD()gVD( objectobjectwateroil ⋅⋅=⋅⋅+⋅⋅
objectobjectwateroil VD)VD()VD( ⋅=⋅+⋅
( ) ( )oil water object object
V A h
D V D V D V
= ×
× + × = ×

29. • If d is the height of the object (the 4 cm in
the figure), let y = the portion of the object
in the more dense liquid and d-y = the
portion of the object in the less dense
liquid.
• This equation can then be solved for the
unknown variable.
( ) ( )oil water object objectD A d y D A y D V× × − + × × = ×

30. Pressure ExamplePressure Example
• Water is to be pumped to the top of the Empire StateWater is to be pumped to the top of the Empire State
Building, which is 366 m high. What gauge pressure isBuilding, which is 366 m high. What gauge pressure is
needed to raise the water to a height of 366 m? Theneeded to raise the water to a height of 366 m? The
density of water is 1000 kg/mdensity of water is 1000 kg/m33
..
Pa3586800
m
N
3586800P
s
m
9.8
m
kg
1000m366P
gDhP
2
23
==
⋅⋅=
⋅⋅=

31. Buoyant ForceBuoyant Force
• An object weighing 300 NAn object weighing 300 N
in air is immersed inin air is immersed in
water after being tied to awater after being tied to a
string connected to astring connected to a
balance. The scale nowbalance. The scale now
reads 265 N. Immersedreads 265 N. Immersed
in oil, the object appearsin oil, the object appears
to weigh 275 N.to weigh 275 N.
• A. Find the density of theA. Find the density of the
object.object.
333
2
air
air
33
3
OHair
m
kg
8571.5
m10x3.5714
kg30.61
D
kg30.61
s
m
9.8
N300
g
Fw
m
gmFw
m10x3.5714V
.
m
kg
1000
N35
gD
BF
V
gVDBF
N35N265N300BF
FwFwBF 2
==
===
⋅==
=
⋅
=
⋅
=
⋅⋅=
=−=
−=
−
−
V
m
D
s
m
2
89

32. Buoyant ForceBuoyant Force
• B. Determine the density of the oil.B. Determine the density of the oil.
3
2
33
33
oilair
m
kg
.
s
m
9.8m10x3.5714
N25
gV
BF
m10x3.5714V
displacedfluidofvolumeobjectofvolume
gVDBF
N25N275N300BF
FwFwBF
9714=
⋅
=
⋅
=
=
=
⋅⋅=
=−=
−=
−
−
D