Bernoulli lab report
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ABSTRACT
The experi experimen mentt was conduct conducted ed in order order to demons demonstra trate te Bernoul Bernoulli` li`ss Theore Theorem m to investigate validity of Bernoulli`s Theorem when applied to the steady flow of water in tapered duct and to measure the flow rates and both static and total pressure heads in a rigid convergent or divergent tube of geometry for a range of steady flow rates. In fluid dynamics, Bernoulli principles states that for an viscid flow, an increase in the speed of the fluid occurs silmutaneously with a decrease in pressure or a decrease in the fluid potential energy . In order to demonstrate Bernoulli`s Theorem , model FM!" Bernoulli appara apparatus tus test is used used in this this experim experiment ent .The water water flow flow rate rate is measure measure by using using volumetric method . The time to collect #$ water in the tan% was measured. $astly ,the flow rate , velocity , and by using continuity e&uation to find the velocities and find the difference of the velocities were calculated using the data of the results and from the data given .Based on result ta%en it has been analysed that the velocity of the fluid is increase when it flowing from wider to narrower tube regardless the type of flow and pressure different. The velocity is increase as the pressure different is increase for all types of flow. The veloci velocitie tiess differ different ent is a posit positive ive value value that that shown shown this this experim experiment ent is valid valid for bernoulli`s e&uation.
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INTRODUCTION
Bernoulli’s theorem, in fuid dynamics fuid dynamics is the relation among the pressure, velo veloci city ty,, and and elev elevat atio ion n in a movi moving ng fuid fuid whic which h are are liqu liquid id or gas, gas, the the compressibility and viscosity which is internal riction o which are negligible and the fow o fow o which is steady, or laminar. (aniel Bernoulli ,1!"#$ . Bernoulli%s principle is named ater the &wiss scientist aniel Bernoulli who published his principle in his boo' ydrodynamica in 1!"#. )n the 1!**s, aniel Bernoulli investiga Bernoulli investigated ted the orces present present in a moving fuid The British engine engineer er 'sborn 'sbornee (eynold (eynoldss verify verify the existe existence nce of these these lamina laminarr , transi transilat lation ion and turbulent flow regimes by in)ecting some dye strea%s into the flow in a glass pipe .
+amina +aminarr fow is charac character terie ied d by smooth smooth stream streamlin lines es and highly highly order ordered ed motion . -hen the fows is laminar , the dye strea' orms a straight and smooth line at low velocities and when the fow become turbulent , it has a burs burstt o fuctu fuctuat atio ion n in the the tran transi siti tion onal al regi regime me and and iq iq ag ag rapi rapidl dly y and and randomly. (./engel ,2**0$ In fluid dynamics, dynamics, Bernoulli principles principles states that for an viscid viscid flow, flow, an increase increase in the speed of the fluid occurs silmutaneously with a decrease in pressure or a decrease in the flui fluid d pot potenti ential al ener energy gy .* +.en .enge gell , !-- !--// .Berno .Bernoull ulli’s i’s rinci rinciple ple can can be
demo demons nstr trat ated ed by the Bern Bernou oull llii equa equati tion on.. he he Bern Bernou oull llii equa equati tion on is an appro3 appro3imate imate relation relation between between pressur pressure, e, velocity, velocity, and elevation. elevation.-hile -hile the /ontinuity equation relates the speed o a fuid that moving through a pipe to
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states that the sum o the pressure, the potential, and 'inetic energy per unit volume is equal to a 53ed constant at any point o a fuid. Bernoulli%s principle can be e3plained in terms o the law o conservation o energy energy..
he wor' done done by corre correspo spondi nding ng volumes volumes in the wider wider and
narrower pipes will be e3pressed by the product o the pressure and the volume. &ince the speed is greater in the narrower pipe, the 'inetic energy o that that volume volume is great greater er.h .hen, en, by the law o conser conservat vation ion o energ energy, y, this this increase in 'inetic energy must be balanced by a decrease in the pressure4 volume product, or, since the volumes are equal, by a decrease in pressure . Bernoulli6s heorem emonstration 7odel 8 97 2: apparatus consists o a clas classi sica call ;enturi enturi made made o clea clearr acry acryli lic c . seri series es o wall wall tapp tapping ings s allo allow w measureme measurement nt o the static static pressure pressure distribution distribution along the converging converging duct , while a total head tube is provided to traverse along the centre line o the test est sec sectio tion . hese hese tap tappin pings are conn connec ecte ted d to a mano manome mete terr ban' an' inco incorp rpor orat atin ing g a mani manio old ld with with air air blee bleed d valv valve. e. res ressu suri ria ati tion on o the the manometers is acilitated by a hand pump. his unit has been designed to be used with a ydraulics Bench or students to study the characteristics o fow through both converging and diverging sections . uring the e3periment , water is ed through a hose connector and students may control the fow rate o the water by adeglecting elevation differences, differences, so
If the static pressure is p at a point in the flow where the speed is v, then the stagnation pressure, ?o, where the stagnation speed, @o, @o, is is 1ero, may be computed from
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Thus, if the stagnation pressure and the static pressure could be measured at a point, this would give the local flow speed.
9igure ? 8 silmutaneous meas easure urement ment stagnation
o and
static pressure
In Figure ects and consequent head loss between inlet and throat. hereore,
APPARATUS AND MATERIAL
h e ap pa r at u s us ed in th is e3 pe ri me n t ar e Be rn ou ll i’ s pr i nc ip le appa rat us, wei ghi ng tan ', stop stopwa watc tch h and and wate waterr.
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1. 7anome 7anometer ter ubes ubes ". -ater ater )nle )nlett ?. ir Bleed &crew !. Eland nut
9igure8 Bernoulli e3perimental apparatus
5gure8 stop watch 8
venturi meter and the scale
:. nio nions ns 0. ischarge ;alve #.ypodermic probe
@. derence D ; ib 4 ;ic
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Bernoulli Bernoulli’s ’s equation. equation. his e3periment e3periment is based on the Bernoulli’ Bernoulli’s s principle principle which relates between velocities with the pressure or an inviscid fow. Based on the calculation made ater the e3periment, the velocity o the fowing fuid is increased as the fuid fows rom a wider to narrower pipe regardless the pressure di>erence and type o fow o each result ta'en.he result show a rise at each manometer tubes when the pressure di>erence increases. his is shown in all the results tables, where the velocity o water that that fo fows ws in the the tape tapere red d duct duct incr increa ease ses s as the the duct duct area area decr decrea ease ses, s, rega regard rdle less ss o the the pres pressu sure re di>e di>ere renc nce e and and type type o fo fow w o each each resu result lt ta'en.9rom ta'en.9rom the analysis o the results, it can be concluded that the velocity o water decrease as the water fow rate decrease. By using bernoulli equation , result shown that the highest velocity , ; ib is at cross section / which is there is the smaller diameter , 10mm. By using continuity equation , the ;
can be
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determine whether the Bernoulli6s equation is valid or not . Kther than that , Bernoulli6s theorem emonstration emonstration also can be done by using 9141* hydraulic bench and 9141? bernoulli6s apparatus test. )n our e3periment , there must be some paralla3 error and ero error occurs when ta'ing the measurement o each data. he observer must have not not read read the the leve levell o stat static ic head head prop proper erly ly.. 7ore 7oreov over er,, the the eyes eyes are are not not perpen perpendi dicul cular ar to the water water level level on the manome manometer ter.. hus, hus, this this erro errorr will will contribute to the di>erent in the values obtained. Besides that , there are air bubbl bubble e trappe trapped d in the tube and the manome manometer ter that give give some some error error to pressure ta'en .hereore, there are some minor e>ects on the calculations due due to the the erro errors rs . Kthe Ktherr than than that that,t ,the he read reader ers s must must ta' ta'e the the accu accura rate te reading reading rom the manometers. manometers. )n order order to get the accurate value, value, the water level must be let to be really stable. hus, a patient is needed in order to run
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time ta'en or "+ water collected increase and the fow rates o the water decre decrease ased. d. his his e3per e3perime iment nt is consid consider er as a succes successu sull ll as long long as , the di>erences between the ; ib 4 ;ic is positive value. RECOMMENDATION
here are some recommendation in order to obtain more accuracate result in this e3periment. Therefore, through this experiment it is re&uire to ma%e sure that all the apparatus are functioning well. There is no lea%s in the gaps
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9rederic . 7iller, gnes 9. ;andome, Lohn 7cBrewster , Bernoulli6s rinciple , 2*1* , lphascript ublishing, Eiles, M.;., M.;., Avett,L.B. and /heng +iu, &chaumm’s Kutline &eries heory and roblems roblems o 9luid 7echanics and ydraulic, 1@@: , 7cEraw ill )ntl.. engel, P.+. *!-;-/. Fluid *!-;-/. Fluid Mechanics Fundamental and Application. >ew Application. >ew Por%. Mc Craw 9ill. 5ng . Mohammed P.Mousa P.Mousa , 9ydraulic lab investigation of bernoulli`s theorem , Islamic Jniversity , Q access on !< :eptember !-;" R http==site.iuga1a.edu.ps=mymousa=files=5xperimentAGAhydraulicsAlabA.pdf
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