Introduction to Fluid Mechanic
Introduction to Fluid Mechanic CE 321
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This 27 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 27 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 21 Pipe Flow Laminar and Turbulent Flows Pipe Flow a A P1 2 1 2 b Open Channel Flow Circular pipe Cu culnr pipes can withstand large 3 pressure difference helween lhe n u Inside and the outside Without undergoing any signi cant distortion Recmgum but lmncn39culnr plpes cannot ducl Air 12 alm Pipe System Components Averaie Velocity in a Pipe IiI VmgAr HIU AA A R J pur MI I pz1r2m39 11 R A 7 0 Mr D A quotFRquot R w u I u Turbulcm ow Laminar ow Laminar and Turbulent Flow 5 KH 0 1 ram a r quotquot aquotka b ax g J Tramil39mal Smhmllrmrdcd n antsanus r bbm i k J Tu buh l 339 Ilul Laminar and Turbulent Flow Depends on flow rate or the Reynolds number Flow in a round pipe iS I39dllllll39dl ll me s 2100 Flow is turbulent if Re gt 4000 Transitional if 2100ltRelt4000 Turbulent Flow Boundary Layer Boundary Layer REEL Center Lamina Tulbulent Layer Unsteady Velocity is zero at the surface no slip D Distance mm wall 1 Boundary Layer 1 Velocity vector Free stream k Boundarwaver thickness Wall 1F 7 r r 5quot JET Ve nciw Entrance Region amp Fully Developed Flow imam ream flaw I humsew cue V r If Fully val1pm a39lmv39 k Ell T 43 Q l l 39 r39 6 39 il imJhl 39I l l hillI rammed V rm Tyi39li Demimlrng flaw Ml 39 a Fullydeveloped region Balance between pressure and viscous forces Entrance Developing Kegion Balance between pressure viscous and inertia acceleration forces since the fluid accelerates in this region as the velocity profile adjusts to fullydeveloped conditions More complex to analyze Pry Entrance flow F Entrance pressure I drop Fully developed flow apax constant Pressure distribution along a horizontal pipe Magnitude ofthe pressure gradient is larger in the entrance region compared to the fullydeveloped region Irromliunul covet Velocity houuduly Developing Velocin Fully developed ow region layer profile velocity pro le V V V V Hydrodyumnimlly fully developed region The development of lhe velocily E m 0quot E F a E E 2 o E u m u 0 but somewhat alter or fuller in uu39bulent ow Elllmllce region i 7w T Tn Tll T 4 lt lt 4 Velocity boundary layer V t avg X Fully devclaped Entrance region legion LI The val imion of wall shear su39ess in the ow Llil39eclion for ow ill n pl from lhe emrance region into ll developed region 13 e fully Entrance Region amp Fully Developed Flow The shape of the velocity profile depends on whether the flow is laminar or turbulent N e Re Laminar Flow 6 2 Rel6 Turbulent Flow o Fullydeveloped Laminar Flow veIVVILy PIOIIIVO IO quulleu to answer questions about pressure drop head loss flow rate etc For laminar flow Fma can be applied to a fluid element Fullydeveloped Laminar Flow Read section 821 i luwj XU IIJIF39lIS lll 11 turn 39 l39lnnrnesnt iil 1mm r 5 39IL 39l l l J I I ll 39l r K 3 39 39 Ir N l quot i quotTquot quotquot l 39 i F 1 x A i t V nli II i l 1 l l l quot133 Pressure is constant across any crosssection but varies with distance along pipe We apply the equation FX maX 0 since fluid is not accelerating We only need to consider a balance between pressure and viscous forces Laminar Flow r2nrf P1 AP I I amp 21 Z r V average veIOCIty flow 2139 WI rate cross sectional area I D QA 41239 A W p D du du Ap 239 u gt r dr dr 2ul ApD2 7rD4 V Z A 32m Q 128m p Nonhorizontal Pipes Laminar Flow Ap ylsin6D2 7rAp lsin 9D4 VJ 32y 128g Navier Stokes Equations When F ma is applied to a general fluid flow not just pipe flow the governing equations are called NavierStokes Equa ons Fullydeveloped Turbulent Flow Turbulent Flows Turbulent flow is chaotic random flow We use timeaveraged quantities instead of the instantaneous values to calculate fluxes etc Rates will be much higher compared to laminar flow Turbulent Flows t0T u I uxyztdt T to z 77 Eddy viscosity 2 du 2 2 du 239 Z2 turb 0 nme Mixing length concept
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