Chapter 6 Fluid Mechanics Pham Hong Quang

7/26/2019 Chapter 6 Fluid Mechanics Pham Hong Quang

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Fundamental of Physics

PETROVIETNAM UNIVERSITY

FUNDAMENTAL SCIENCE DEPARTMENT

Hanoi, August 2012

Pham Hong QuangE-mail: [email protected]


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Chapter 6 Fluid Mechanics

Pham Hong Quang Fundamental Science Department 2

6.1 Some Basic Concepts

6.2 Pressure

6.3 Variation of Pressure with Depth

6.4 Pressure easurements

6.! Pasca"#s Princip"e6.6 Buo$ant %orces an& 'rchime&es#s

Princip"e

6.( %"ui& D$namics

6.) Stream"ines an& the *+uation ofContinuit$

6., Bernou""i#s *+uation

6.1- (Optional) Other Applications of

Bernou""i#s *+uation


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Densit$ Speci/c 0rait$

The mass density of a substance is the mass ofthe substance divided by the volume itoccupies:

unit: kg/m3

for aluminum 2700 kg/m3or 2.70

g/cm3mass can be written as m

! and weight as mg

!gSpeci/c 0rait$

substance /

water

V

m=


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" bottle has a mass of 3#.00 g when empty

and $%.&& g when 'lled with water. (hen

'lled with another )uid* the mass is %%.7%

g. (hat is the speci'c gravity of this other

)uid+

Take the ratio of the density of the )uid to that

of water* noting that the same volume is

used for both li,uids.( )

( )fluid fluid fluid

fluid

water water water

88.78 g 35.00 g0.877

!8. g 35.00 g

m V mSJ

m V m

= = = = =

Densit$ Speci/c 0rait$

eamp"e


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5he three common7 states orphases of matter

1. So"i& -as a de'nite volume shape.

aintains its shape si1e approimately4*

even under large forces.

2. 8i+ui&-as a de'nite volume* but not a

de'nite shape. 5t takes the shape of its

container.

3. 0as -as neither a de'nite volume nor a

de'nite shape. 5t epands to 'll its container.


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%"ui&s -ave the ability to )ow.

' 9ui&is a collection of molecules that

are randomly arranged held together by

weak cohesive forces by forces eerted

by the walls of a container.

Both liquids & gases are uids

%"ui&s


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6.2 Pressure


"ny )uid can eert a force perpendicular to its

surface on the walls of its container. The force

is described in terms of the pressure it eerts*

or force per unit area:

6nits: /m2or 8a 9 8ascal4

1 atm = 1.013 x 105Pa or 15 lbs/in2 (;ne

atmosphere is the pressure eerted on us

every day by the earths atmosphere4

:ote that pressure is a sca"ar

A

F

p =


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6.2 Pressure



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Experiental !act Pressure&epen&s on &epth.See /gure.5f a static )uid is in acontainer* all portions of the )uidmust be in static e,uilibrium.

"ll points at the same depth must

be at the same pressure;therwise* the )uid would not bestatic.

sectional area '?tends from depth &to & ; hbelowthe surface

The li,uid has a density

"ssume the density is the samethrou hout the )uid. This means it is


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There are three eternal forces acting on the darker

region. These are:The downward force on the top* P-'

6pward force on the bottom* P'

@ravity acting downward* g

The mass can be found from the density:

The net force on the dark region must be 1ero:

g = -

Aolving for the pressure gives

P = P-; gh

Ao* the pressure Pat a depthh below a point

in the li,uid at which the pressure is P-is

M V Ah = =


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*arth#s atmosphere" )uid.But doesnt have a 'ed top CsurfaceDE


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. ressure easuremens


" possible means of measuringthe pressure in a )uid is tosubmerge a measuring devicein the )uid." common device is shown in

the lower 'gure. 5t is anevacuated cylinder with a pistonconnected to an ideal spring. 5tis 'rst calibrated with a known

force."fter it is submerged* the forcedue to the )uid presses on thetop of the piston compressesthe spring.

The force the )uid eerts on the


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6.4 Pressure Measurements


anomet

er

Bour&on

5ue


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Diaphragm


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Capsu"e


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6.5 Pascals Principle


f an eterna" pressure is app"ie& to a

con/ne& 9ui& the pressure at eer$ pointwithin the 9ui& increases $ that amountE


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6.5 Pascals Principle



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6.6 Buoyant Forces and Archimedess Principle


This is an object submerged in a fluid. There is a

net force on the object because the pressures at thetop and bottom of it are different.

The buoyant force is found to be

the upward force on the same

volume of water:


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The net force on the object is then the

difference between the buoyant force and thegravitational force.


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If the objects density is less than that of water,

there will be an upward net force on it, and it willrise until it is partially out of the water.


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or a floating object, the fraction that is submerged

is given by the ratio of the objects density to that ofthe fluid.


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This principle also wor!s in

the air" this is why hot#air

and helium balloons rise.


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6.7 Streamlines and the Equation of Continuity


'n ideal uidis assume&

$to be incompressible so that its density does

not change4*

$to )ow at a steady rate*

$to be nonviscous no friction between the

)uid and the container through which it is

)owing4* and

$)ows irrotationally no swirls or eddies4.


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If the flow of a fluid is smooth, it is called streamline

or laminar flow %a&.

'e will deal with laminar flow.

The mass flow rate is the mass that passes a given

point per unit time. The flow rates at any two pointsmust be e(ual, as long as no fluid is being added or

ta!en away.

This gives us the e(uation of continuity:


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If the density doesnt change ) typical for li(uids

) this simplifies to . 'here the pipe is

wider, the flow is slower.

10-9 Bernoullis Equation


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10-9 Bernoulli s Equation


* fluid can also change its

height. +y loo!ing at thewor! done as it moves, we

find:

This is +ernoullis e(uation.

ne thing it tells us is that as

the speed goes up, the

pressure goes down.



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10-9 Bernoulli s Equation


Proof ofBernoullis Equation

(ork has to be done to make the )uid )ow


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" very large pipecarries water with avery slow velocityand empties into a

small pipe with ahigh velocity. 5f 82is

7000 8a lower than89* what is the

velocity of thewater in the smallpipe+

3.(4 m@s

10 9 B lli E ti


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"#$

$

$

$

%

$$%

AA

pAv

=

Venturi %"ow

eter

10 9 B lli E ti


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et force onwing+

G "Hv22I v9

24

Hair 9.2$

kg/m3

10 9 B lli E ti


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Cure Ba""

10 9 B lli E ti


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10 9 B lli E ti


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'tomiFer

"s air passes at top of tube*the pressure decreases and )uid is drawnupthe tube.

10 9 B lli E ti


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(ater drains out ofthe bottom of acooler at 3 m/s*

what is the depthof the water abovethe valve+

4!., cm


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Than% #ou

Documents

Chapter 6 Fluid Mechanics Pham Hong Quang