Bernoulli's Theorem, Limitations & its Practical Application

Bernoulli's Theorem, Its Limitations & its practical applications (Pitot Tube, Venturi Meter & Orifice Meter)... By Engr. M. Jalal Sarwar

2. BERNOULLI’S THEOREM
•Itstates“foraperfectincompressibleliquid,flowinginacontinuous
stream,thetotalenergyofaparticleremainsthesame,whiletheparticle
movesfromoneparttoanother”.Thisstatementisbasedonthe
assumptionthattherearenolossesduetofrictioninthepipe.
Mathematically
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2
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+
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=??????�������

3. LIMITATIONS OF BERNOULLI’S THEOREM
1.TheBernoulli’sequationderivedbyassumingthatthevelocityofevery
elementoftheliquidacrossanycrosssectionofthepipeisuniform.
Practicallyitisnottrue.
2.TheBernoulli’sequationhasbeenderivedundertheassumptionthatthe
externalforce,exceptthegravityforce,isnotactingontheliquid,butin
actualpracticeitisnotso.Therearealwayssomeexternalforcesactingon
theliquidwhicheffecttheflowoftheliquid.
3.Bernoulli’sequationhasbeenderivedontheassumptionthatthereisno
lossofenergyoftheliquidparticlewhileflowing.Infact,somekinetic
energyisconvertedintoheatenergy&someenergyislostduetoshear
force.
4.Ifaliquidisflowinginacurvedpath,theenergyduetocentrifugalforceis
neglected.

4. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
•TheBernoulli’sequationisthebasicequationwhichhasthewidest
applicationsinHydraulics.Thisequationisappliedforthederivationof
manyformulasandhydraulicdevices.ThoughtheBernoulli’sequationhas
anumberofpracticalapplicationsbutthefollowingarethemostlyused
hydraulicdevicesontheprinciplesofBernoulli’sequation:
1.PitotTube
2.OrificeMeter
3.VenturiMeter

5. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
1)PITOTTUBE:
APitotTubeisaninstrumenttodeterminethevelocityofflowatthe
requiredpointinapipeorastream.APitotTubeconsistofaglasstubebent
athrough90
o
.Thelowerendofthetubefacesthedirectionoftheflow.The
liquidrisesupinthetubeduetothepressureexertedbytheflowingliquid.
Bymeasuringtheriseofliquidinthetube,wecanfindoutthevelocityofthe
liquidflow.
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6. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
2)ORIFICEMETER:
AnOrificemeterisusedtomeasurethedischargeinpipe.AnOrificemeter
consistsofaplatehavingasharpedgedcircularholeknownasanOrifice.The
plateisfixedinsideapipe.Amercurymanometerisconnectedwithittoknow
thedifferenceofpressurebetweenthepipe&thethroatorinotherpipe.
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�
1−�
2
�
1
2
−�
2
2
2??????ℎ
Q=Discharge,C=Co-efficientofOrificemeter,
�
2=AreaofOrifice,g=GravitationalAcceleration,
h=Pressuredifferenceofliquidhead,�
1=AreaofPipe

7. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
3)VENTURIMETER:
AVenturimeterisanapparatusforfindingoutthedischargeofaliquid
flowinginapipe.AVenturimeterconsistsofthefollowingthreeparts:
a)ConvergingCone:itisashortpipewhichconvergesfromdiameterof
thepipetoasmallerdiameter(Throatdia).Itslengthistakenupto2.5
timesthediaofpipe.Theslopesofconvergingsidesisbetween1:4to
1:5.ItisalsocalledinletofVenturiMeter.
b)Throat:ItisthemiddlesmallerportionoftheVenturimeter.Itsdiais
keptconstant.Itsdiameteristakenupto¼to½ofthediameterofthe
pip.

8. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
3)VENTURIMETER:
c)DivergingCone:itisapipe,whichdivergesfromathroatdiametertoa
largerdiameterofpipe.Thedivergentconeisalsoknownasoutletof
theVenturimeter.Thelengthofthedivergentconeisabout3to4times
thanthatoftheconvergentcone.
Venturimetercanbeconnectedwithpipehorizontally&vertically.Inboth
states,thedischargecanbefoundby:
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�
1−�
2
�
1
2
−�
2
2
2??????ℎ
C=ConstantofVenturimeter(0.97avgValue),k=Co-efficientofOrifice
Meter,�
1=AreaofPipe,�
2=AreaofThroatoftheVenturiMeter

9. VENTURIMETER
PRACTICAL APPLICATION OF BERNOULLI’S THEOREM