Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 19 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 9 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 9 Bernoulli Equation Pressure Probes F ma along a streamline sin 8p I 93 V81 93 Bernoulli Equation 1 p E pV2 72 constant along a streamline Physical Interpretation 1 p l Epl2 l 72 constant 2 p V l l 2 Constant 2 Hl 7 9 Elevation W 39 Head Pressure Veloc1ty Head Head The sum of the pressure head the velocity head and the elevation head is constant along a streamline Limitations of Bernoulli s Equation Steady Flow Frictionless Flow No Shaft Work Incompressible Flow No Heat Transfer Flow along a Streamline Qwewwe Do Not Use Bernoulli s Law Here Sudden Long and narrow expansion tubes 6 D gt gt Flow through a valve A heating section Static Stagnation Dynamic amp Total Pressure Stagnation Pressure Pressure at the Stagnation Point 39 W Newman smmw D C 425 UhltS p pvz 72 constant Each term has dimensions of force per unit area p is the actual thermodynamic pressure called static pressure Open Static relative to moving fluid pV22 is called the dynamic pressure gt yz is the hydrostatic pressure PTstatic dynamic hydrostatic gt Why is pV22 called the dynamic pressure Open Consider pressure at the end of a small tube inserted into the flow pointing upstream Liquid fills tube to a height H after initial transients have died out Velocity of fluid in tube and at the tip is zero Applying Bernoulli formula 9 P at stagnation point is greater than the static pressure p1 by an amount pV22 the dynamic pressure Pitot Tube Pitot Tube If we know the static and stagnation ressures we can calculate the fluid speed 7 Two concentric tubes Inner tube measure 1 2 stagnation pressure 193 p Epl Outer tube measures 194 p1 1 static pressure 2ltp3 p4 F ma Normal to a Streamline Z Fn 6mp V R v2 a quot R 26F 6W l 5F 7COS9 6V n 1 9n PV2 Vdn 9n R v2 1 dn 72 301181331113 across the streamline 317 Several holes are punched into a in can as shown in Fig 13317 See Video V35 Which of the gurcs rcpruscms the van ation of the water velocity as it leaves the holes Justify your choice a b c 317 solution Zz cansfanf sv 74 wM 1401 sa and 2h J 2 7 a 7 free surface MM 4 J 7 239I 4g7 21 9 47 1910 free jevlJaM Z72 0quot 7 gm w 7 14 Vamph 557 Th 15 Vz h Him 3 CurHMquot dz sfv bu m MATLAB Code hO00lO25 IV E SIMULINK vsqrt20981h plotvh 39row seugca 39Adlr39 39reverse39 99 so we have zo at the top xlabel39Veloc1ty ms39 ylabel39Depth from the free surface m w m o O o A ow JV 0 N Depth from me free surface 0 1 1 5 2 2 5 Ve ocwty ms 323 A re hose nozzle has a diameter of 1 in According to some re codes the nozzle must be capable of delivering at least 300 galmin If the nozzle is attached to a 3ii11diameter hose what pressure must be maintained just upstream of the nozzle to deliver this owrate A Brass Fire Hose 323 Solution 0 3 in z z lz v z biz125 wM zz J g a in If3 39 3 and Q 300 7219723 g 0quot 9 2139 7704 t J z quot 0 3 Viz VI J 6 4 39 797 Jffffijf f 95339 f allot 0 H3 056 y 7 a T 39 35 i E 3 L quot so 7 542 WM P 3977 H M ngequl 87 0M 342 The speci c gravity of the manometer uid shown in Fig P342 is 107 Determine the volume l lowrate Q if the ow is inviscid and incompressible and the flowing uid is a water b gasoline or c air at standard conditions l T I Q 009m diameter 1 En IT l39 O 3quot a 10 mm L V