MSC Software MSC.EASY5 Governing Equations Conservation of mass Conservation of energy Conservation of momentum Flowlpressure drop correlations for pipes and orifices Pipe friction factors as a function of Reynolds number EAS103 Fluid Power Systems Advanced Class-Chart 11
MSC.Software EAS103 Fluid Power Systems Advanced Class - Chart 11 MSC.EASY5TM Governing Equations • Conservation of mass • Conservation of energy • Conservation of momentum • Flow/pressure drop correlations for pipes and orifices • Pipe friction factors as a function of Reynolds number
MSC Software Conservation of mass MSC.EASY5 dt (pv) out In fluid property terms 1 aP aP. dp dt out pv) x If energy transfer is ignored P 1 aP dt out-pv or the more familiar β OP EAS103 Fluid Power Systems Advanced Class-Chart 12
MSC.Software EAS103 Fluid Power Systems Advanced Class - Chart 12 MSC.EASY5TM Conservation of Mass or dt d P dt dP T dt dT = + fluid property terms If energy transfer is ignored, or the more familiar in out P · Q Q V · = ( – – ) dt d (V win wout ) = – +V in wout = w – dρ dt dV dt β V dP P · win wout V · ( – – T · = = ) – × 1 P V ρ P . ρ ρ T dt dP P · win wout V · = = ( – – ) 1 P V ρ dt P ρ β =
MSC Software MSCEASY5 Conservation of Energy (pVu) d(pVh)=2(wh).2(wh, ) entering leavin Ing conducted or generated Enthalpy and internal energy rates are practically the same for liquids (For gases, a rigorous formulation uses the definition of enthalpy, h=u-p/r) Since enthalpy is a function of temperature only, it can be replaced with temperature 2=CP12 ~△Pw十HA△T generated conducted EAS103 Fluid Power Systems Advanced Class-Chart 13
MSC.Software EAS103 Fluid Power Systems Advanced Class - Chart 13 MSC.EASY5TM Conservation of Energy • Enthalpy and internal energy rates are practically the same for liquids. (For gases, a rigorous formulation uses the definition of enthalpy, h = u - P/r.) • Since enthalpy is a function of temperature only, it can be replaced with temperature: h · 2 T h 2 T · 2 c P T · = = 2 generated conducted Qf DP w = +HAΔ T ( ) dt d ( ) Vh ( ) whi ( ) whj - f = + entering leaving conducted or generated Q dt d Vu
MSC Software MSCEASY5 Conservation of momentum Transient Form A(P-P)w (w M22 R2m 准+ 2PAD PAL pressure force shearforce convective velocity max(W1,0) min(WR2, 0) f=friction factor=g(Re, d) Note that w, is a state variable EAS103 Fluid Power Systems Advanced Class-Chart 14
MSC.Software EAS103 Fluid Power Systems Advanced Class - Chart 14 MSC.EASY5TM – w Conservation of Momentum, Transient Form w · 2 A P 1 P 2 ( ) – L w2 w2 × 2ADh – ×f w1M 2 w2 w2 ( ) × R2m 2 – AL = + pressure force shear force convective velocity w1M max (w1 = ,0) wR2m min (wR2 = ,0) f = friction factor = g(Re,d) Note that w2 is a state variable
MSC Software MSCEASY5 Conservation of Momentum, Steady state Form At steady state R2 For example, for pipe flow, 「f When f is a function of w2 the flow regime is considered The steady-state form Is usually adequate for most models, unless waterhammer pressure or flow surges is a major concern Introduces artificially high frequencies that are completely damped EAS103 Fluid Power Systems Advanced Class-Chart 15
MSC.Software EAS103 Fluid Power Systems Advanced Class - Chart 15 MSC.EASY5TM Conservation of Momentum, Steady State Form At steady state, = 0, w1 = w2 = wR2 dw dt For example, for pipe flow, w2 A Dh fL = 2 DP sgnDP When f is a function of w2 , the flow regime is considered. The steady-state form . . . • Is usually adequate for most models, unless waterhammer pressure or flow surges is a major concern • Introduces artificially high frequencies that are completely damped