2013 Lect1 Application of Fluid Static

8/13/2019 2013 Lect1 Application of Fluid Static

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Fluid Statics

The word statics is derived from Greekword statikos= motionless

For a fluid at rest or moving in such a manner

that there is no relative motion between

particles there are no shearing forces

present:

Rigid body approximation


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STATIC FLUID APPLICATION

Vessel thickness design,Measurement of pressure,

Separation of fluids with different density,

Hydraulic jack

Design of ship


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Principle of Fluid Static

P = P0+ rgdF = rg V

P = F/A

05


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Mass per unit volume (e.g., @ 20 oC, 1 atm)

Water = 1000 kg/m3

= 62.3 lbm/ft3

Mercury = 13,500 kg/m3

Air = 1.22 kg/m3


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Density Densities of gasses increase with pressure

Densities of liquids are nearly constant (incompressible) for constanttemperature

Specific volume = 1/density

950960970980990

1000

0 50 100Temperature (C)

Density(kg/m3)


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API gravity is an alternative method of comparing the

densities of different petroleum substances. The API

system of gravity measurement has units called 'Degrees

API' (API). The device used for the measurement of API

and specific gravity is the 'HYDROMETER'.


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Specific gravity = {Brix/(258.6-[Brix/258.2]*227.1)}+1

Brix and specific gravity refer to the amount of

sugar in a water solution. Commonly used in

beer and wine making, the amount of sugar in

the unfermented wort (for beer) or must (for

wine) determine the level of alcohol in the

finished product.


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API gravity is calculated from the Specific Gravity as

follows: -

API = (141.5 SG) - 131.5

Example 2: An oil has an API gravity of 42.0. Calculate its S.G.

S.G. = 141.5 (131.5 + 42) = 141.5 173.5 = 0.816 SG

From the above formulae, it is found that pure water (S.G. = 1.000) has an API gravity of 10.

As fluid density decreases, the API gravity increases.


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Specific Gravity

Ratio of fluid density to density water at

specified T dan P (e.g., @ 20 oC, 1 atm)

3/9790 mkgSG

liquid

water

liquidliquid

r

r

r

Water SGwater= 1

Mercury SGHg= 13.6

Air SGair= 1

3/205.1 mkgSG

gas

air

gasgas

r

r

r


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TEKANAN

Gaya per satuan luas, dimana gaya tegak lurus luasan.

p=A m2

Nm-2

(Pa)

NF

patmosfir= 1.013X105Nm-2Pa (Pascal)

1psi = 6895 Pa


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0F

Hydrostatic Pressure

F = gaya dari atas + gaya dari bawah + gaya gravitasi = 0

0 zyxgyxPyxP ba r

gz

PP bar

Tekanan atasPb

Tekanan bawah

Pa

Za

Zb

Densitas=r

z

gdz

dPr


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Incompressible fluidLiquids are incompressible i.e. their density is assumed to

be constant:

PghP or

By using gage pressures we can simply write:

ghP r

)zz(gPP 1212 r

Pois the pressure at the

free surface (Po=Patm)

When we have a liquid with a free surface the pressure P at any depth below the free surface is:


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Units for Pressure

Unit Definition orRelationship

1 pascal (Pa) 1 kg m-1s-2

1 bar 1 x 105Pa

1 atmosphere (atm) 101,325 Pa

1 torr 1 / 760 atm

760 mm Hg 1 atm

14.696 pounds per

sq. in. (psi)

1 atm


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Tekanan pada permukaan air danau adalah 105 kPa.

Hitung tekanan pada kedalaman 35.0 m dibawah

permukaan air.

atm3.4kPa343

m35m/s8.9kg/m1000

23atm

atm

dgPPP

dgPP

r

r

Kerapatan air segar


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hydrostatic

The pressure in a homogeneous, incompressible fluid atrest depends on the depth of the fluid relative to some

reference plane, and it is not influenced by the size or

shape of the tank or container

Fluid is the same in all containers

Pressure is the same at the bottom of all containers

h


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Tekanan di permukaan planet Venus adalah 95 atm.

How far below the surface of the ocean on Earth do

you need to be to experience the same pressure?

m950

N/m109.5m/s8.9kg/m1025

N/m109.5atm94

atm1atm95

2623

26

atm

d

d

dg

dg

dgPP

r

r

r

Density of sea water


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KEDALAMAN OIL RESERVOIR

What the depth

below the surface

of oil reservoir

that produce oilwith relative

density 0.8 and

wellhead pressure

of 120 kN/m2?

rwater = 1000 kg/m3, and p atmosphere = 101kN/m2.


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Vertical plane surfaces

F

Vertical rectangu lar wall (wall wid th = W)

H

h

Here the pressure varies

linearly with depth: P=rgh

P

The lock gate of a canal is rectangular, 20 m wide and 10m high. One side is exposed to the atmosphere and the

other side to the water. What is the net force on the lock

gate?


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Vertical plane surfaces For an infinitesimal area dA the normal force due to the

pressure is

dF = p dA

Find resultant force acting on a finite surface by

integration

Whdhg r dAPF

For vertical rectangular wall: F = r g W H2

dhhgW r


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Storage Tanks

They are used in a variety

of industries like

Petroleum refiningChemical

Power

Food & beverage

Pharmaceutical


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MAIN COMPONENTS OF

PRESSURE VESSEL

Following are the main components of pressure

Vessels in general

Shell

Head

Nozzle

Support


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SHELL

Horizontal drums have cylindrical shells and

are constructed in a wide range of diameter

and length.

The shell sections of a tall tower may be

constructed of different materials, thickness

and diameters due to process and phase

change of process fluid.

Shell of a spherical pressure vessel isspherical as well.


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HEAD

All the pressure vessels must be closed at

the ends by heads (or another shell section).

Heads are typically curved rather than flat. The reason is that curved configurations are

stronger and allow the heads to be thinner,

lighter and less expensive than flat heads.

Heads can also be used inside a vessel andare known as intermediate heads.

These intermediate heads are separate

sections of the pressure vessels to permit

different design conditions.


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NOZZLE

A nozzle is a cylindrical component that

penetrates into the shell or head of pressure

vessel.

They are used for the following applications.

Attach piping for flow into or out of the vessel.

Attach instrument connection (level gauges,

Thermowells, pressure gauges).

Provide access to the vessel interior atMANWAY.

Provide for direct attachment of other equipment

items (e.g. heat exchangers).


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SUPPORT

Support is used to bear all the load of

pressure vessel, earthquake and wind loads.

There are different types of supports which

are used depending upon the size and

orientation of the pressure vessel.

It is considered to be the non-pressurized part

of the vessel.


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structure must be designed to resist deformation and collapse under allthe conditions of loading. The loads to which a process vessel will be subject

Major loads

1. Design pressure: including any significant static head of liquid.

2. Maximum weight of the vessel and contents, under operating conditions.3. Maximum weight of the vessel and contents under the hydraulic test conditions.

4. Wind loads.

5. Earthquake (seismic) loads.

6. Loads supported by, or reacting on, the vessel.

As a general guide the wall

thickness of any vessel should not be less than the values given below; the values

include a corrosion allowance of 2 mm:Vessel diameter (m) Minimum thickness (mm)


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The cross-sectional area is pi times the diameter squared divided by 4.

The cross-sectional area of tank A is:

The volume V is A x H:

The weight of the water WAis:

Therefore the pressure is: This is the pressure in pounds per square feet, one more step is required to get the

pressure in pounds per square inch or psi. There is 12 inches to a foot therefore there

is 12x12 = 144 inches to a square foot.

The pressure p at the bottom of tank A in psi is:


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PRESSURE MEASUREMENT

Many techniques have been developed for themeasurement of pressure and vacuum. Instruments

used to measure pressure are called pressure gauges

or vacuum gauges.

A manometercould also be referring to a pressuremeasuring instrument, usually limited to measuring

pressures near to atmospheric. The term manometeris

often used to refer specifically to liquid column

hydrostatic instruments.

A vacuum gaugeis used to measure the pressure in a

vacuum


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ABSOLUTE, GAUGE AND DIFFERENTIAL PRESSURES

Absolute pressureis zero-referenced against a

perfect vacuum, so it is equal to gauge pressure plus

atmospheric pressure.

Gauge pressureis zero-referenced against ambientair pressure, so it is equal to absolute pressure minus

atmospheric pressure. Negative signs are usually

omitted.

Differential pressureis the difference in pressure

between two points.


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ABSOLUTE AND GAGE PRESSURE

ABSOLUTE PRESSURE: The pressure of a fluid is

expressed relative to that of vacuum (=0)

GAGE PRESSURE: Pressure expressed as the

difference between the pressure of the fluid and that ofthe surrounding atmosphere

gageatmabs PPP


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atmospheric pressures, deep vacuum pressures must be absolute

Atmospheric pressure is typically about 101.325 kPa or 100

kPa or 30 inHg at sea level, but is variable with altitude and

weather.

a vacuum of 26 inHg gauge is equivalent to an absolute

pressure of 30 inHg (typical atmospheric pressure) 26 inHg =

4 inHg.

Tire pressure and blood pressure are gauge pressures by

convention


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Measurement of Pressure

Manometers are devices in which one or

more columns of a liquid are used to

determine the pressure difference

between two points.

U-tube manometer

Inclined-tube manometer


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A manometer

is a U-shaped

tube that is

partially filled

with liquid.

Both ends of the

tube are open to theatmosphere.

The difference in fluid height in a liquid column

manometer is proportional to the pressure difference.

THE U-TUBE MANOMETER.

Liquid column


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Measurement of Pressure Differences

mambb

mmba

gRZgPP

RZgPP

rr

r

)(

)(

3

2

Apply the basic equation of static fluids to both legs of

manometer, realizing that P2=P3.

)( bamba gRPP rr


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A t i f i t d t d f th U t b


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Cylinderof gas

A container of gas is connected to one end of the U-tube

C

BB

A d

gdP

gdPPPP

gdPPP

BCB

CBB

r

r

r

gauge

atm

'

B'B PP

atmc PP

Point A is the original location of the

top of the fluid before the gas

cylinder is connected.


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Using a u-tube manometer to measure gauge pressure of fluid density 700

kg/m3, and the manometric fluid is mercury, with a relative density of 13.6.What is the gauge pressure if:

a). h1 = 0.4m and h2 = 0.9m?

b) h1 stayed the same but h2 = -0.1m?

THE U-TUBE MANOMETER.

I li d M


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Inclined Manometer

To measure small pressure differences need to magnifyRmsome way.

rr sin)(1 baba gRPP


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Measurement of Pressure

The atmospheric pressure can be measured with a barometer.

For mercury barometers atmospheric pressure

(101.33kPa) corresponds to h=760 mmHg (= 29.2 in)

If water is used h = 10.33 m H2O (= 34 ft)

vaporatm pghp r

Th B d


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The Bourdon pressure gauge uses the principle that a flattened tube tends to change to be

straightened or larger circular cross-section when pressurized. Although this change in

cross-section may be hardly noticeable, and thus involving moderate stresseswithin the

elastic range of easily workable materials, the strainof the material of the tube is magnified

by forming the tube into a C shape or even a helix, such that the entire tube tends tostraighten out or uncoil, elastically, as it is pressurized

The Bourdon pressure gauge

Bourdon tubes measure gauge pressure, relative to ambient

atmospheric pressure
http://en.wikipedia.org/wiki/Stress_%28mechanics%29http://en.wikipedia.org/wiki/Deformation_%28mechanics%29http://en.wikipedia.org/wiki/Gauge_pressurehttp://en.wikipedia.org/wiki/Gauge_pressurehttp://en.wikipedia.org/wiki/Deformation_%28mechanics%29http://en.wikipedia.org/wiki/Stress_%28mechanics%29


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Stationary parts:

A: Receiver block. This joins the inlet

pipe to the fixed end of the Bourdon

tube (1) and secures the chassis plate

(B). The two holes receive screws that

secure the case.

B: Chassis plate. The face card is

attached to this. It contains bearing

holes for the axles.

C: Secondary chassis plate. It

supports the outer ends of the axles.

D: Posts to join and space the two

chassis plates.

Moving Parts:

Stationary end of Bourdon tube. This communicates

with the inlet pipe through the receiver block.Moving end of Bourdon tube. This end is sealed.

Pivot and pivot pin.

Link joining pivot pin to lever (5) with pins to allow joint

rotation.

Lever. This is an extension of the sector gear (7).

Sector gear axle pin.

Sector gear.

Indicator needle axle. This has a spur gear thatengages the sector gear (7) and extends through the

face to drive the indicator needle. Due to the short

distance between the lever arm link boss and the pivot

pin and the difference between the effective radius of

the sector gear and that of the spur gear, any motion of

the Bourdon tube is greatly amplified. A small motion of

the tube results in a large motion of the indicatorneedle.

Hair spring to preload the gear train to eliminate gear

lash and hysteresis.
http://en.wikipedia.org/wiki/Hysteresishttp://en.wikipedia.org/wiki/Hysteresis


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Schematic drawing of a

simple mercury barometerwith vertical mercury column

and reservoir at base

Barometers


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Atmospheric pressure is equivalent to a

column of mercury 76.0 cm tall.

gdP r


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Temperature variation with altitude for the U.S. standard atmosphere

COMPRESSIBLE FLUID

Gases are compressible i.e. their density varies with temperature and

pressurer =P M /RT


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For small elevation changes (as in engineering applications,tanks, pipes etc) we can neglect the effect of elevation on

pressure

o

o

RT

zzgpp

Tfor

)(exp

:constT

0

0

g

dz

dpr

CONSTANT Temperature

r

RT

p

V

M

M

RTnRTpV


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Linear Temperature Gradient

)( 00 zzTT

z

z

p

p zzT

dz

R

g

p

dp

00 )( 00

Rg

T

zzTpzp

0

00

0

)()(


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Atmospheric Equations

Assume linear

Rg

TzzTpzp

0

000 )()(

Assume constant

0

0 )(

0)( RT

zzg

epzp

Temperature variation with altitude

for the U.S. standard atmosphere


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Compressible Isentropic

v

p

CC

Pconstant

P

g

rr gg

1

1y

PP

TT

1

11

g

1

12

1

1

12

11

11

RT

zgMTT

RT

zgMPP

g

g

g

ggg

Application: bottom hole conditions in gas wells


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Separation of fluid with different densiti

How it works

GRAVITY DECANTER


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AAAAbB ZZZ

BalancecHydrostati

rrr 21 A

B

A

BTA

A

ZZ

Zr

r

r

r

1

2

1

When BAinterface location is very sensitive to height of heavy liquid overflow leg. This leg is often has

adjustable height to give the best separation.


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DECANTER

It is proposed to use a gravity decanter toseparate a light petroleum oil (density 50.0lbm/ft3) from water (density 62.3 lbm/ft3). Its

desire to maintain a total depth of 30 in. in thevessel and to have exactly equal depth of oil andwater. What should be the height , expressed ininch of the water discharge leg above the bottom

of the vessel.


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Centrifugal decanters

When the density difference between two immiscible liquids is small gravitation forces may be too weak

to separate them in a reasonable time. In this case we can use centrifugal forces to amplify the forces

exerted on the liquids.

Centrifugal separations are important in many food industries such a breweries, vegetable oil

processing, fruit juice processing. They are also used to separate emulsions into their components.

Hydrostatic Equilibrium


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in a Centrifugal Field

2

2

60

2

NmrmrFc

mgFg2

60

2

N

g

r

F

F

g

c

Typically N1000 and r1m. Fc/Fg110. Neglect g.



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in Centrifugal Field

dmrdF

ratdrelementonForce2

drrbdm r2

drrbdF22

2 r

21222

12

2

2

2

rrPP

drrrb

dFdP

r

r

Continuous Centrifugal


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Decanter

?Why

PPPP BiAi

AB

BA

BA

i

rr

r

r

r

r

r

1

22



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DecanterConsequences:

ABwithin 3% riunstable

rBconstant rAincreased rishifted toward bowl wall

In commercial units rAand

rBare usually adjustable

Example


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Example

Consider a 90 elbow in a 2 in. pipe. A pipe tap is drilled through the wall of the elbow on the inside

curve, and another though the outer wall directly across from the first. The radius of curvature of the

inside bend is 2 in. and that of the outside of the bend is 4 in. The pipe is carrying water, and amanometer containing an immiscible oil with S.G. of 0.90 is connected across the two taps. If the

reading of the manometer is 7 in., what is the average velocity of the water in the pipe?


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Design of hydraulic jack


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Direction of fluid pressure on boundaries

Furnace duct Pipe or tube

Heat exchanger

Dam

Pressure is a Normal Force(acts perpendicular to surfaces)

It is also called a Surface Force

In a fluid confined by solid boundaries, pressure acts

perpendicular to the boundaryit is a normalforce.

P l P i i l


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Pascals Principlethe Principle of transmission of fluid-pressure

"pressure exerted anywhere in a confined incompressible fluid is

transmitted equally in all directions throughout the fluid such that

the pressure ratio (initial difference) remains the same


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The 1 pound load on the 1 square inch area causes an increase in pressure on the fluid in

the system. This pressure is distributed equally throughout and acts on every square inch

of the 10 square inch area of the large piston. As a result, the larger piston lifts up a 10

pound weight. The larger the cross-section area of the second piston, the larger themechanical advantage, and the more weight it lifts.

when there is an increase in pressure at any point in a confined fluid, there is an equal

increase at every other point in the container.


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Gaya force F1

bekerja pada piston A1

.

1

1

22

2

2

1

1

A

A

A

F

A

F

2pointat1pointat

FF

PP

F2

1 500 N

10 5000 N

100 50,000 N

12 AA

F1= 500 N


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A hydraulic press has an input cylinder 1 inch in diameter and an output

cylinder 6 inches in diameter.

Assuming 100% efficiency, find the force exerted by the output piston

when a force of 10 pounds is applied to the input piston.

If the input piston is moved through 4 inches, how far is the outputpiston moved?

Exercises:

a. 360 pounds

b. 1/9 inch


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The input and output pistons of a hydraulic jack are

respectively 1 cm and 4 cm in diameter. A lever

with a mechanical advantage of 6 is used to apply

force to the input piston. How much mass can thejack lift if a force of 180 N is applied to the lever

and efficiency is 80%?

Exercises:

1410.6 kg


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Design of Ship

Th b t f


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The buoyant force

When an object is placed in a fluid, the fluid exerts an upward force we call

the buoyant force.The buoyant force comes from the pressure exerted on the object by the

fluid. Because the pressure increases as the depth increases, the pressure

on the bottom of an object is always larger than the force on the top - hence

the net upward force.

F1

F2

h1

h2

H

Buoyancy


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Buoyancy

The net force due to pressure in the vertical direction is:FB= F2- F1= (Pbottom- Ptop) (xy)

The pressure difference is:

PbottomPtop= rg (h2-h1) = rg H

Combining:

FB= rg H (xy)

Thus the buoyant force is:

FB= rg V

Buoyant Force (FB) weight of fluid displaced

ARCHIMEDES PRINCIPLE


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FB= rfluidVdisplaced gFg= mg = robject Vobjectgobject sinks if robject> rfluid

object floats if robject< rfluidobject floats if rfluid = robject


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COBA PIKIRKAN


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1. Go up, causing the

water to spill out of

the glass.

2. Go down.

3. Stay the same.

COBA PIKIRKAN

B =rW g Vdisplaced

W =rice gVice rW g V

Must be same!

ice-cube

Sebuah balok es mengambang diatas

segelas air, sampai permukaan air ratapada pinggiran.

Ketika es meleleh maka air di dalam

akan :

ARCHIMEDES EXAMPLE


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ARCHIMEDES EXAMPLE

A cube of plastic 4.0 cm

on a side with density

= 0.8 g/cm3is floating

in the water.

When a 9 gram coin is

placed on the block,

how much sinks belowwater surface?

h

koin

ARCHIMEDES EXAMPLE


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ARCHIMEDES EXAMPLE

mg

Fb

Mg

SF = m a

FbMgmg = 0

rg Vdisp= (M+m) g

Vdisp= (M+m) / r

h A = (M+m) / r

h = (M + m)/ (rA)

= (51.2+9)/(1 x 4 x 4) = 3.76 cm

M = plasticVcube = 0.8x4x4x4

= 51.2 g

h

koin

W d h i 4 b d d t dii i d l


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m5.1

m10*m20kg/m1000

kg100.3

0

3

5

A

m

d

mAd

mV

gmgVgm

wF

wFF

w

b

bw

bww

bwww

B

B

r

r

r

r

Wadah segi 4 berdasar datar diisi dengan coal,

massanya 3.0105 kg. Panjang 20 m dan lebar 10m,

mengambang diair. Berapa kedalaman wadah masuk ke

dalam air.

w

FB


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Sepotong logam dilepaskan

dibawah air water. Volume

metal 50.0 cm3dan SG 5.0.

Hitung percepatan initialnya,saat v=0 tidak ada gaya drag.

w

FB


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2013 Lect1 Application of Fluid Static

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Transcript of 2013 Lect1 Application of Fluid Static