Formal Reportx (1)

8/18/2019 Formal Reportx (1)

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TITLE

Bernoulli Theorem

OBJECTIVES

1. To demonstrate Bernoulli Theorem through a venturi meter.2. To investigate the relationship between the pressure head and

velocity head along a venturi meter.

THEORY

Bernoulli Theorem indicates that, if an inviscid fluid is flowing along apipe of varying cross section,then the pressure is lower at constrictions where thevelocity is higher, and higher where the pipe opens out and the fluid stagnates.

Many people find this situation paradoxical when they first encounter it

(higher velocity, lower pressure). The well-nown Bernoulli e!uation is derivedunder the following assumptions"1.Fluid is incompressible; density, ρ is constant

2.Flow issteady,

δ = 0

δ t

3. Flow is friction less,τ =04.Flow is along a streamline.

Then it is expressed with the e!uation (1)

p

ρg+

v2

2g + z=constant (1)

where p # fluid static pressure at the cross section in $%m&

ρ # density of the flowing fluid in g%m'

g # acceleration due to gravity in m % s& (its value is .1 m % s&)

v # mean velocity of fluid flow at the cross section in m%s z # elevation of the center of the cross section with respect to z # *

h + # total (stagnation) head in m

The term on the left-hand-side of the aove e!uation represent the pressurehead ( p ρ g ),

velocity head

(v2

2 g ), and elevation head ( z ), respectively. The sum of theseterms is

nown as the total head ( h +).


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ccording to the Bernoulli theorem of fluid flow through a pipe, the total

head h+at any cross-section are constant(ased on assumptions givenaove).owever,in a real flow due to friction and other imperfections, as well asmeasurement uncertainties, the results may deviate from the theoretical one.

/hen the centerline of all cross-sections that are considered lie on thesame

ori0ontal plane(which we may choose as thedatum, 0eros so that the aove e!uationreduces to"

z =0),and thus,all the z values are


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'

p

ρg+

v2

2g=h=constant

This is the total head at the cross-section.

z =0),andthus,allthe z valuesar


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APPARATUS

1. Bernoulli’s Theorem Apparatus CT-1801-5-BT

2. !"rauli# Ben#h CT-1801

PR$C%&UR%

1. The 'ater mass (lo'rate 'as set at 5 )* min +! turnin) the ,al,e appropriatel!. This

#an +e seen (rom the s#ale o( the (lo' meter or at an! maimum a#hie,a+le ,alue.

2. The nut 'as pushe" to "is#har)e the air in the pressure tappin) assem+l! so that the

'ater le,el 'ill rise. t is re#ommen"e" that the 'ater le,el is to +e in the mi""le ran)e o( the

pressure tappin).

3. Rea"in)s o( "i((erential pressure "rop alon) the ,enturi meter (or tappin) num+er 1/

2/ 3/ / 5/ / an" 8 'as re#or"e".

. B! "is#ar"in) pro#e"ure 2/ pro#e"ure 1 to 3 'ere repeate" (or lo'er mass (lo' rates

o( )* min/ 3 )* min/ 2 )* min an" 1 )* min/ +! a"ustin) the ,al,e.


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%4P%R%6TA7 &ATA

Ta+le 1 Pressure "rop alon) the lon)itu"inal pro(ile o( the enture meter

low rate 2enturiTappings

1 & ' 3 4 5 6

4g%min(&*7%min) &5& &33 16 136 1 &&* &35 &'

3g%min(147%min) &34 &'' 1 155 &** &15 &&5 &&

'g%min(1*7%min) && &&& &*1 11 &*1 &*' &16 &1

& g% min (6 7% min) &14 &1' &*& 1& &*& &* &1* &1&

1 g% min (3 7% min) &*4 &*3 &** 16 &*1 &*' &*3 &*3

Plot a )raph o( these "i((erential pressures a)ainst the lon)itu"inal pro(ile o( the enturimeter


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&SCUSS$6

1. 9hat is the relationship +et'een ,elo#it! an" #ross se#tional-area: ;usti(! !our

ans'er.

The smaller the #ross-se#tional area o( the tu+e/ the hi)her the ,elo#it!..

2. 9hat is the relationship +et'een pressure an" ,elo#it!: ;usti(! !our ans'er

The lo'er the pressure o( the li


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$ther (lo' meters 'hi#h utilie the same prin#iple as a mean o( (lo' measurement

are Pitot tu+e an" ?lo' tu+e.

C$6C7US$6

Base" on the eperiment #on"u#te" the Bernoulli’s Theorem is pro,en 'here an in#rease in

,elo#it! is a##ompanie" +! a "e#rease in pressure.. ?urthermore/ the Bernoulli’s Theorem has

su##es(ull! "emonstrate" throu)h the ,enturi meter in this e.

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