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Experiment 4: Flow through Orifices

Abstract

This experiment is measured in the reduction on contraction of fluids in a current

and its lost of energy when water is discharged through an orifice in the tanks base. A

series of procedures were taken in the laboratory, varying the flow of water some

elevations were maintained and measures were taken of the tank, the pilot tube and the

diameter of the water current. Also, the reason for flow using a hydraulic tank and taking

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three measurements for no more than a certain amount of time was determined.

Comparing the data with different diameters orifices was determined as well. The

objective was to determine the coefficients of velocities, contraction and discharge since

the acceleration and the diameter of flow depends on such matter.

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Table of Content

Abstract..!

"ist of #igures...$"ist of Tables.%

&ntroduction...'

Theory...()!!

*+uipment escription.!-)!'

esults!()-/

iscussion...$0

Conclusion...$!

ecommendations.$-

eferences..$$

Appendix

*xample of Calculus..$'

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Introduction

The reduction of flow is given by the currents concentration this is one of the

experiments objectives. This occurs when a fluid passes through an orifice and the

current flows through it as well the discharge is less than the amount calculated

assuming that the energy is conserved.

&n this experiment, the student will measure the extent of the reduction in the flow

contraction of the stream and energy loss, as water discharges into the atmosphere

from an orifice in the base of tank. #urthermore, the student can compute coefficients of

velocity and contraction for set of five different orifices.

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F E

or

) F F

y substituting in ernoullis e+uation, we find the velocity at T to be

%

This is the "&ealvelocity at T, based on constant total head along the streamline.

The same result applies to all streamlines of the flow, so choosing the symbol to

denote this ideal velocity, we find

F G%.-H

This result is often called Torr"#ell"'( theore).

=ear the orifice, the fluid accelerates toward the center of the hole, so that as the

jet emerges it suffers a reduction of area due to the curvature of the streamlines. The

reduction of area due to this local curvature may be taken to be complete at about half

the orifice diameter downstream of the orifice the reduced section is usually called the

vena contracta as shows in #igure %.-.

The ideal velocity the contracted section is seen to be that which is ac+uired

by a body falling from rest gravity through a height

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Figure 4!

Ideal and "ena Contracta #et Flow through an Orifice

ecause of the energy loss, which takes place as the water passes down the

tank and through the orifice, the a#tual velocity, the plan of the vena contracta is

smaller than . A pilot tube placed in the stream at the contracted section will record a

value by

F G%.$H

Clearly G represent the energy loss. The ratio of actual velocity and ideal

velocity is often called the velocity coefficient of the orifice.

F G%.%H

&n similar since, the concentration coefficient is defined as the ratio of contracted area

to orifice area .

F F G%.'H

#inally, the discharge coefficient is defined as the ratio of the actual discharge to the

ideal discharge.

F G%.(H

or

F .

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The actual discharge is

F F G%.3H

and the ideal discharge is given by

F F F . . G%.BH

9o the actual discharge may be written as

F . G%./H

and by using e+uations G%.%H to G%.BH

F F F . G %.!0H

4*3 Co!tra#te& Coeff"#"e!t "! Flow throuh Or"f"#e a!& +o,,le

#igure %.$ shows fluid streaming through a smoothly contracting noDDle which

produces a parallel jet. The overall increase in speed through the concentration reduces

the effect of any non)uniformity which might exist in the approaching flow, so if is

reasonable to assume that the fluid velocity is sensibility uniform across the emerging

jet. 9ince the cross)sectional area of the jet is the same as that of the noDDle, the rate of

flow may be obtained simply by multiplying the noDDle area by the speed of the jet. &n

#igure %.$ GbH and #igure %.$ GcH however, the fluid does not emerge in parallel fashion

but as a convergent stream, so that the cross)sectional area of the jet reduces to a so)

called contracted section or vena contracta. :ver this section the streamlines are

parallel. 7oreover, the velocity is effectively uniform over the contracted section. The

flow rate may now be obtained by multiplying the area of the contracted section by the

fluid speed over it.

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There are no theoretical values of the coefficient, as the amount of head loss

and the concentration of the stream may be found only by experiments. 2owever, there

is a theoretical contraction coefficient for inviscid flow though a two)dimensional sharp

edged slit. The result is F IJ GI E -H K 0.(!!

Concentration coefficient values for different exit geometries are shown below.

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4*4 -e(#r".t"o! of the Or"f"#e /..aratu(

#igure %.' shows the arrangement of the apparatus which is designed to be used

with the 2ydraulic ench described in 5nit !. The water tank is fed from the bench

supply through an adjustable vertical pipe ended in a diffuser just below the water

surface. An overflow pipe directs the surplus water to the drain outlet in the bench top.

The orifice under tests is fitted into the base of the tank, and the emerging jet passes

through the bench top into the measuring tank of the bench. A top in the base of the

tank connects with a manometer tube. This manometer is mounted in front of a vertical

scale and shows level of water in the tank above the plane of orifice. A second

manometer tube is connected to a 8ilot tube, which may be introduced into the

discharging jet to measure the total head. &f may be traversed across the jet by

revolving a graduated nut which works along a lead screw of ! mm. the diameter of the

jet may be measured by traversing a sharp blade, supported in the 8ilot tube, from one

side of the jet to the other.

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Equipment Description

1* ra")etr"# y&raul"# e!#h

It is used to for measuring the volumetric flow of water at a certain given time.

Figure 4$: %ra&imetric 'ydraulic (ench

! )ater "al&e

sed to control the flow of water !eing "um"ed into the tan#.

Figure 4*: )ater "al&e

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+ ,tart -ump (utton

$llow electric current to start the "um" for the fluid transfer.

Figure 4.: ,tart -ump (utton

4 )eights

Itis used to determine the weight of the water. %he weight&!eam has 1'3 ratio.

Figure 4/: )eights

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0 Thermometer

sed to measure the tem"erature of the water.

Figure 412: Thermometer

$ Chronometer

In this e("eriment its function is to measure the time that the weigh&!eam ta#es to get to

its hori)ontal "osition* on the "oint of !alance !etween the weights and the mass of the

li+uid in the tan#.

Figure 411: Chronometer

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* Orifice Apparatus

$""aratus designed to !e used with h,draulic !ench to create a flow contraction "attern*

of which a contraction coefficient will !e determined.

Figure 41!: Orifice Apparatus

. -itot Tube

%he -itot tu!e is a sim"le and convenient instrument to measure the difference !etween

static* d,namic and total "ressure or head/. It can measure the fluid flow velocit, !,

converting the #inetic energ, in the fluid flow into "otential energ,.

Figure 41+: -itot Tube

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ater flow

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T/E 5:E.er")e!tal -"(#hare Coeff"#"e!t for the Or"f"#e

Ob(*=olu)e

flow rate)3?(

1?2

)1?2

=olu)e flowrate >actual

)3?(

-"(#hareCoeff"#"e!t

C&

1 0.000$3 0.(!/(B $.('*)0% 0./B(('

2 0.000$' 0.'/!(! $.%/*)0% 0.//'3/

3 0.000$% 0.'3%%( $.$B*)0% 0.//'$(

4 0.000$$ 0.''(3B $.-B*)0% 0.//$/(

5 0.000$0 0.'!-B% $.0-*)0% !.0!''3

6 0.000-/ 0.%/(// -./$*)0% !.00/(!

7 0.000-/ 0.%B%33 -.B(*)0% 0./B%3B

8 0.000-B 0.%3B'% -.B-*)0% !.0--'B

9 0.000-3 0.%'-33 -.(3*)0% 0./B!0%

10 0.000-% 0.%0$3$ -.$B*)0% 0.//!0-

Oerall /erae % C&% 0./3($

(lo.e m% 0.000(

+or)al",e&alueC&%

!.0!B%3

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O3IFICE !

ater Te).erature: -%.% LC Or"f"#e -"a)eter -0: 0.0!$ m

-e!("ty: //3.-% kgJm

$

Cro(( e#t"o!al Or"f"#e area /0: 0.000!$$ m

-

T/E 6:-ata of Flow Rate$ ea&$ a!& et -"a)eter for the E.er")e!tal Or"f"#e

Ob(*

Or"f"#e ;ea(ure)e!t ra")etr"# Flow ;ea(ure)e!t

0))

C))

-C))

e"h;a((

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Or"f"#e

Ob(*=olu)e flow

rate)3?(

1?2

)1?2

=olu)e flowrate >actual

)3?(

-"(#hareCoeff"#"e!t

C&

1 0.000$( 0.(!3 $.(%*)0% !.00!$!'

2 0.000$' 0.'/0 $.%B*)0% 0.//-/$/3 0.000$% 0.'B! $.%-*)0% !.003$'0

4 0.000$! 0.'-( $.!0*)0% !.000!B$

5 0.000$! 0.'-0 $.0(*)0% 0./B3%(%

6 0.000$0 0.'!0 $.00*)0% !.00!$0'

7 0.000-/ 0.%/! -.B/*)0% 0.//3-(3

8 0.000-B 0.%3% -.3/*)0% 0.//B00/

9 0.000-( 0.%%3 -.($*)0% !.0!$$!!

10 0.000-% 0.%03 -.%0*)0% !.000!0!

Oerall /erae % C&% 0.////-'

(lo.e m% 0.000(

+or)al",e&alueC&%

!.0!B%3

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ORIFICE 3

ater Te).erature: -' LC Or"f"#e -"a)eter -0: 0.0!$ 7

-e!("ty: //3.0%( kgJm$ Cro(( e#t"o!al Or"f"#e area /0: 0.000!$$ m-

T/E 1:-ata of Flow Rate$ ea&$ a!& et -"a)eter for the E.er")e!tal Or"f"#e

Ob(*

Or"f"#e ;ea(ure)e!t ra")etr"# Flow ;ea(ure)e!t

0))

C))

-C))

e"h;a((

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T/E 4:E.er")e!tal -ata of Or"f"#e ;ea(ure)e!t( about Co!tra#te& e#t"o!

Ob(*0GmH

C)

-C)

C= CC C&

1 0.$(/ 0.$(' 0.0!$ 0.//%'3 !.00000 0.//%'3

2 0.$%$ 0.$%! 0.0!$ 0.//30B 0./-%'( 0./-!B(

3 0.$!' 0.$0' 0.0!$ 0./B%00 0./B%(3 0./(B/-

4 0.-B% ) ) ) ) )

5 0.-'$ ) ) ) ) )

6 0.-!' ) ) ) ) )

7 0.!BB ) ) ) ) )

8 0.!33 ) ) ) ) )

9 0.!(B ) ) ) ) )

10 0.!%% ) ) ) ) )

T/E 5:E.er")e!tal -"(#hare Coeff"#"e!t for the Or"f"#e

Ob(*=olu)e

flow rate)3?(

1?2

)1?2

=olu)e flowrate >actual

)3?(

-"(#hareCoeff"#"e!t

C&

1 0.000$( 0.(03%' $.'B*)0% 0.//%0(

2 0.000$' 0.'B'(( $.%'*)0% 0./B'3B

3 0.000$$ 0.'(!-' $.$!*)0% !.00!/%

4 0.000$! 0.'$-/- $.!%*)0% !.0!-3%

5 0.000$0 0.'0-// -./(*)0% 0.//(03

6 0.000-3 0.%($(B -.3$*)0% !.0!!3!

7 0.000-( 0.%$$'/ -.''*)0% 0./B-%%

8 0.000-' 0.%-03! -.%B*)0% 0.//!%09 0.000-% 0.%0/BB -.%!*)0% !.00(!!

10 0.000-- 0.$3/%3 -.-%*)0% !.0!(!'

Oerall /erae % C&% 0.///B%

(lo.e m% 0.000(

+or)al",e&alueC&%

!.0!B%3

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ORIFICE 4

ater Te).erature: -' LC Or"f"#e -"a)eter -0: 0.0!$ 7

-e!("ty: //3.0%( kgJm$ Cro(( e#t"o!al Or"f"#e area /0: 0.000!$$ m-

T/E 1:-ata of Flow Rate$ ea&$ a!& et -"a)eter for the E.er")e!tal Or"f"#e

Ob(*

Or"f"#e ;ea(ure)e!t ra")etr"# Flow ;ea(ure)e!t

0))

C))

-C))

e"h;a((

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T/E 3:I&eal Flow Rate throuhOr"f"#e

Ob(*0

GmH

1?2

Gm!J-

H

=olu)eflow rate

Gm$JsH

1 0.$B0 0.(!( 0.000$(

2 0.$'' 0.'/( 0.000$'

3 0.$0' 0.''- 0.000$$

4 0.-B0 0.'-/ 0.000$!

5 0.-'' 0.'0' 0.000$0

6 0.--0 0.%(/ 0.000-B

7 0.-!0 0.%'B 0.000-3

8 0.!B0 0.%-% 0.000-'

9 0.!(' 0.%0( 0.000-%

10 0.!%0 0.$3% 0.000--

T/E 4:E.er")e!tal -ata of Or"f"#e ;ea(ure)e!t( about Co!tra#te& e#t"o!

Ob(*0GmH

C)

-C)

C= CC C&

1 0.$B0 $30 0.0!- $!.-0$/! 0.B'-03 -(.'B3/'

2 0.$'' $%' 0.0!! $!.!3%-0 0.3!'/B --.$!///

3 0.$0' -/$ 0.0!- $0.//%%' 0.B'-03 -(.%0/%3

4 0.-B0 ) ) ) ) )

5 0.-'' ) ) ) ) )

6 0.--0 ) ) ) ) )

7 0.-!0 ) ) ) ) )

8 0.!B0 ) ) ) ) )

9 0.!(' ) ) ) ) )

10 0.!%0 ) ) ) ) )

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Conclusion

After the experiment of #low through an :rifice was realiDed, it was concluded

that is was satisfactory success because if the fluid undergoes a change in evaluation

pressure at the bottom of the tube the pressure is greater than at the top and it will

determine the speed with which raises the fluid in the orifice. &t was determine that the

velocity of the tanks phase was negligible and that the atmospheric pressure was

outstanding. 9ince the pressure decreases and the speed increases, that less energy is

lost and the values that obtained experimentally discharge coefficient and the values of

this did not fold !, which shows the accuracy the taking of measures. #inally it is

concluded that were the speed increases the fluid will make greater flow volume.

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Recommendation

&n order to save time, coordinate the steps in the procedure with your group in

order to obtain the results from the experiment faster.

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Reference

lackboard "earning 9ystem, http1JJonlinecampus.pupr.eduJ

#luid 7echanics "aboratory 7anual, epartment of 7echanical *ngineering,

8olytechnic 5niversity of 8uerto ico

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Examples of Calculus

1. ass low

a.

2. olumetric low

a.

0 0.000355

0 3.6(10&4

!.

3. ormali)ed alue

a.

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