Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 23 page Class Notes was uploaded by Jolie Shields on Saturday September 19, 2015. The Class Notes belongs to CE 321 at Michigan State University taught by Roger Wallace in Fall. Since its upload, it has received 17 views. For similar materials see /class/207369/ce-321-michigan-state-university in Civil Engineering at Michigan State University.
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Date Created: 09/19/15
Lecture 10 Applications of Bernoulli Equa on Energy Grade Line Bernoulli Equation 1 p V2 72 constant 3 2 2 p V a zconstant y Elevation LYquot 39 Head Pressure Velomty Head Head 1 1 p1 PEUV 721 2 p2 510V22 722 Piezometer It measures static pressure Free Jets Between Points 1 and 2 1 2 h V 7 2 P 0 Q V0 Between Pomts 3 and 4 p3 vh l p3gtltvlgtlt pn2p4 pw 39V237 The vena contracta effect Inability of the fluid to turn a 1 sharp 90 corner E Conttaotion Coefficient g r A CC Lquot mutant Ah E Confined Flows Fluid is confined in a device so pwsswe is not known a priori Use the law of conservation of mass continuity equation Conservation of Mass mpQ gt wA m1mz pA1V1PA2V2 Venturi gt A Venturi is a system for speeding the ow of the uid by constrictu a com shaped tube found in many applications where the speed of the uid is important and forms the basis of devices like a carburetor carburetor Mixes air wi gasoline vapor prior to explosion The carburetor works on Bernoulli39s pllllclple the fact that moving air has lower pressure than still air Pressure and Velocity Changes in kinetic V energy are often I w accompanied by changes In f 1 2 1 pressure m I 5 15mm 0 Flowrate Measurement Principle Place a flow restriction in the pipe Measure pressure difference between the low velocity high pressure region upstream and the high velocity low pressure region 1 1 P1 PWP2 pr QVlA1 VgAy Sluice Gate Measure discharge in open channel ows 1 1 101pr 721p2 pV22 722 Q AM Wl V242 Im p1p20 c a C mum c Pitot Tube Pt total pressunz f static pressure pressm lo lube transduczr PS 9 Piezometer Head Sum of pressure head and elevation head Energy Line and Hydraulic Grade Line EL is a line that represents the total ead available to the fluid This can be obtained by measuring the stagnation pressure with a Pitot tube Hence is the locus f elevations measured using a series of Pitot tubes The locus mea s f piezometer taps static elevation is called the HGL ELamp HGL Z 2 0 Vfzg HGL I EGL gt gt gt gt x 1 Diffuser 2 3 Arbitrary reference plane z O EL amp HGL EL is always a distance V2 29 above the HGL They approach each other as velocity decreases The EL is horizontal under the assumptions on tile Dernoulli equation If the fluid velocity changes along a streamline then the HGL will not be horizontal Bernoulli Equation Restrictions Flow is steady Fluid is incompressible application to gases can introduce errors The stagnation pressure is gt the static pressure by pV22g if density remains constant This dynamic P varies as V2 Irror Increases WItn tne square or tne velocity Rule of thumb lncompressible if Mach is lt 03 Ma Vc ckRT12 for standard air lnviscid flow no viscous effectsl Water ows through the branching pipe shown in Fig If viscous effects are negligible determine the pressure at section 2 and the pressure at section 3 Along be dreaminc from I fo 1 FM wad z wherezzz 0 and Iquot I 31 1f 1 3 xxx0 Tils 3 1 300x10 IVmquot lams 2 Hms 790x103 Mm3 2191mzs ZROXo Mm3 248 0231 or 5 A thOS mz p1 252m 71 252 kP 331 3 v2 14 mS A2 003 m 50 0 11 2 AS 0 035 m2 3 10m Continued 3 V214ms 42003 m2 2o Ala9 Me dreamins from I 1 0 3 H 2 4quot739 Z 1 3 33 where since 0 0 03 7 u 034W 6262z win AM 0 Md g 0quot sz 07 003In74n75 m V A 0035mquot 39quot6 77113 571 becomes th Z0J 2340 aaoxla Almz 0 ms2 mm5f p3 Ham 990x103Vm3 2q9lm 990xm3Vm3 2149Ims W 5 lfx0 M1 2 ltPa Problem 355 p 99 355 Water ows under the inclined sluice gate shown in Fig P355 Determine the owrate if the gate is 8 ft wide 355 solution FIGURE 19355 2 1 fizl zl vzz W E e flUIf20 and 2 If III0 A V 2 V2 2 or A v 6f V2 73fL V 7 I4 6 V 77705 5g I becomes 6 lz2323916H or 1 303 Hence 62 M 6H50H303 1 95 Cavitation Cavitation is the formation of vapor bubbles in a liquid caused by low pressures in the liquid When the local pressure at a point in the liquid falls below the liquid39s vapor pressure the liquid undergoes a phase change to a gas creating quotbubblesquot Causes damage to equipment due to noise Cavitation is a problem in submarines noise destroys stealth Madame g 39 l Mgr g lnupleni cawiaiicn
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