MMVF01 Termodynamik och strömningslära FORMELSAMLING till
Institutionen f¨ or Energivetenskaper MMVF01 Termodynamik och stro ara ¨mningsl¨ FORMELSAMLING till D. F. Young, B. R. Munson, T. H. Okiishi & W. W. Huebsch, A Brief Introduction to Fluid Mechanics, John Wiley & Sons, Inc. Sammanst¨alld av Christoffer Norberg juni 2011 Kapitel 3 — Bernoullis ekvation Betrakta, enligt figuren nedan, en fluidpartikel som f¨oljer en str¨omlinje i tv˚ adimensionell, station¨ar, och friktionsfri str¨omning (endast tryck- och gravitationskrafter). Hastighetsvektor: Vs = V = ds , Vn = 0 dt ∂V V2 Accelerationsvektor: as = V , an = ∂s R dp + ρ d (V 2 /2) + ρ g dz = 0 (l¨angs str¨omlinjen) Inkompressibel stro¨mning ⇒ p + ρ V 2/2 + ρ g z = konst. (l¨angs str¨omlinjen) p = statiskt tryck (faktiskt tryck); ρ V 2 /2 = dynamiskt tryck; ρ g z = γ z = h¨ojdtryck. dz dp ρ V 2 + + ρg = 0 (tv¨ars str¨omlinjen) dn R dn Inkompressibel str¨omning ⇒ p+ρ R V2 R dn + ρ g z = konst. (tv¨ars str¨omlinjen) 1 • Ekvivalent ytr˚ ahet ǫ (nya ro¨r, typiska va¨rden): Material (Sv.) Glas Plast (PVC), draget M¨ assing, draget Rostfritt st˚ al Gummi Kommersiellt st˚ al Smidesj¨ arn Bleckpl˚ at, sl¨ at Galvaniserat j¨ arn Tr¨ a, hyvlat Gjutj¨ arn Betong, glatt Betong, skrovlig Nitat st˚ al Material (Eng.) Glass Drawn tubing Brass, drawn Stainless steel Rubber Commercial steel Wrought iron Tinplate, smooth Galvanized iron Wood, planed Cast iron Concrete, smooth Concrete, rough Riveted steel ǫ [mm] 0.0 (sl¨att) 0.0015 0.002 0.002 0.010 0.046 0.046 0.07 0.15 0.18–0.9 0.26 0.3–0.8 1.2–3.0 0.9–9.0 • Eng˚ angsfo ¨rluster (eng. minor losses) ∆pf ,minor = KL ρV 2 V2 = ρghL,minor ⇒ hL,minor = KL 2 2g ℓ ρ X f R¨ orsystem: ∆pf = ∆pf ,major +∆pf ,minor = 2 i D 2 ! i Vi2 + (8.20) X j (KL)j Vj2 ORDLISTA English absolute pressure adverse pressure gradient average velocity basic dimension boundary layer bulk modulus buoyant force, buoyancy continuity equation control volume Couette flow crude oil density discharge coefficient displacement thickness drag drag coefficient dynamic (absolute) viscosity dynamic pressure elbow entrance region friction factor frontal area gage pressure head loss heat transfer rate hydraulic diameter irrotational flow kinematic viscosity laminar flow linear momentum equation loss coefficient Mach number mass flowrate material (substantial) derivative major loss minor loss moment-of-momentum equation momentum thickness nozzle meter orifice meter pathline pipe flow Pitot-static tube planform area Poiseuille flow svenska absoluttryck (relativt vakuum) ogynnsam tryckgradient medelhastighet prim¨ar dimension gr¨ansskikt bulkmodul (tryckmodul) flytkraft kontinuitetsekvationen kontrollvolym, o¨ppet system Couettestr¨omning r˚ aolja densitet genomstr¨omningskoefficient f¨ortr¨angningstjocklek str¨omningsmotst˚ and motst˚ andskoefficient dynamisk viskositet dynamiskt tryck r¨orb¨oj, r¨orkr¨ok inloppsstr¨acka friktionsfaktor frontarea ¨overtryck (relativt omgivande tryck) h¨ojdf¨orlust v¨armefl¨ode hydraulisk diameter rotationsfri str¨omning kinematisk viskositet lamin¨ar str¨omning impulssatsen eng˚ angsf¨orlustkoefficient machtal (Machs tal) massfl¨ode materiell derivata h¨ojd- eller tryckf¨orlust p.g.a. v¨aggfriktion eng˚ angsf¨orlust impulsmomentsatsen impulsf¨orlusttjocklek strypfl¨ans strypbricka partikelbana r¨orstr¨omning Prandtlr¨or planarea Poiseuillestr¨omning 3 avsnitt 1.5, 2.5 9.2.6 5.1.1, 8.2 7.1 9.2 1.7.1 2.11.1 3.6.2, 5.1, 6.2.1 4.3 6.9.2 1.6, 8.5 1.4.1 8.6 9.2.1 9.1.1 7.9.2, 9.1.1 1.6 3.5 8.4.2 8.1.2 8.4.1 9.1.1 1.5, 2.5 5.3.3 5.3.1 8.4.3 6.1.3, 6.4.3 1.6 4.1.3, 8.1.1 5.2.1/2 8.4.2 3.8, 7.6 5.1.1 4.2.1, 6.1.1 8.4.1 8.4 5.2.3/4 9.2.1 3.6.3, 8.6 3.6.3, 8.6 4.1.4 8.1 3.5 9.1.1 6.9.3 pressure coefficient pressure drag, form drag pump head rate of shearing strain repeating variables Reynolds number separation shaft power shaft torque siphon specific gravity specific volume specific weight speed of sound sluice gate steady flow streakline streamline surface tension system turbulent flow vacuum pressure valve vapor pressure velocity head Venturi meter volume flow rate volumetric dilatation rate vorticity wall shear stress tryckkoefficient formmotst˚ and pumph¨ojd skjuvt¨ojningshastighet repeterande variabler Reynolds tal avl¨osning axeleffekt vridmoment sugh¨avert (h¨avert) relativ densitet volymitet tyngd per volymsenhet ljudhastighet slussport station¨ar str¨omning str˚ aklinje str¨omlinje ytsp¨anning slutet system turbulent str¨omning undertryck (relativt omgivande tryck) ventil ˚ angtryck hastighetsh¨ojd venturimeter volymfl¨ode volymsdilatation vorticitet v¨aggskjuvsp¨anning 4 9.3.2 9.3.2 5.3.3 6.1.3 7.3 7.6 9.1.2/6 5.2.4 5.2.4 3.6.2 1.4.3 1.4.1 1.4.2 1.7.3 3.6.3, 10.6.4 4.1.3 4.1.4 4.1.4 1.9 4.3 4.1.3, 8.1.1 2.5 8.4.2 1.8 3.4 3.6.3, 8.6 5.1.1 6.1.2 6.1.3 8.2.1
© Copyright 2024