fluid_fluid_mechanics_2

fluid_fluid_mechanics_2 - Pressure Pressure: Force per unit...

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Unformatted text preview: Pressure Pressure: Force per unit area (N / m2) acting on a surface. Caused by molecules striking the surface. Pressure force -perpendicular to surface —acts on the surface d1?“ = (—fz)pdA fi = unit normal fiz—[pfidA A Pressure acts in the fluid: i {EEHA 7%"; Fluid and Container Container 5 l E § 5 ’ .é ' = 1 f .-' .' l ' ‘ 1/. if "" ff, j" ,3: 1/ ,i 1"ch W17 If 3/ ' l f: T“? 2 L: a i ' if ‘ Fluid Fluid in Two Parts Pressure in Moving Fluid: ,_ dA Static PressUre = Pressure relative to moving fluid. Equation of State From thermodynamiCs p = f (191 ) 43/9 8/? dP‘gp‘Mw +5T)p 16p _ 1 6(m/V) :_lfi : Z ___)T_(m/v) 8p )T V61)» K Compresszbzlzly 15p __ 1 eon/V) _1av : Z _ [051‘ 19— (m/V) 6T )p_ )1) fl ThermaZExpcmszon ‘v’aT d7'027cdp—fldT $=—de+fldT Water: K=5.8x10*10/(N/m2) ' . fl=1.48x10_4/0K Ap=190atm, %—de=5.8x10‘1°(190)(101000)20.01 AT=1000K, %€%—fldT=~1.48x10—4(100)2—0.015 Liquid Water is Incempressible for mOSt applicatiOHS. (}ases PerfectGas: p : pRT where R = specific gas constant Air: R = 287N-m/kg OK Standard sea level conditions: 19 =lOl,OO()N/m2 T=lSOC : p _____ / 2 p RT 287(15+273) ' gm T ))T:l P P Pfip [32462) name/RD) :1. ,0an 19 8T P T dp dp dT p KP fld p T At standard sea level conditions . K 21/101000 = 9.9x104/(N/m2), fl 21/288 2 3.47x10"3/°K For an isotopic process, p mp7 or 9%? Z 9, £108 With the momentum equation dp = —deV @.=—ideV=—_p.dI/2 ,0 719 2%) For a 2% change in density, we get V=68.6m/S. Air is essentially incompressible for V<70m/ S. Flow Field Characteristics Velocity Vector: I7 = ui + v} + w]; Steady flow: Velocity at each point in space is constant V = V(x, y,z) Unsteady flow: I7 = 17(x, y,z,t) ' Examples: Oscillating flows Start up process Moving vehicle/fixed observer ‘ Observer moving With a vehicle at constant velocity = Steady Velocity measurement from displacement of small particles Particle positic'm ,Particle position at time t \ / at time t+ A: \ ‘ {MM—w /K / V E as / A e W Particle trajectories: u, dy v, 422w g: ~...._.: 6% (a dz‘ Flow Visualization: Particles on a liquid surface Dye streams in liquids Smoke streams in gases One and Two dimensional flows ‘ ' //{ Figure 1.7 Two Dimensional Flow Figure 1.8 One Dimensional Flow Shear stress and friction , AF T=hmrj [SA—>0 ' Figure 1.13 Shear force EVHW ~ 'I - V /:7/ _ / Figure 1.14 Relative motion and shear stress :38 oz Ewing Eggs Egg $5de $33 Ema E m3 3%; sag magma gamma Emma EEE S I ommnm . n_ wUfler muEEmmE 352m») FUNDAMENTAL LAWS ' “FOR A SYSTEM SYSTEM: A defined quantity of matter v Conservation of Matter: ' D/Dt (mass) = O Newton’s Second Law: _ D/Dt (momentum) =. Sum of Forces = Pressure + Gravity + ’ ' _ Friction 4 First Law of Thermodynamics: D/Dt (energy) = Heat Transfer + Work. Done Energy 2 TnternaT + Kinetic APPROACHES ' Analytical: Fundamental. Understanding ' Preliminary Design Experimental: Fundamental Understanding~ Proof of Concept Model Testing Prototype Testing Computational: Fundamental Understanding Design and Testing ...
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This document was uploaded on 07/06/2011.

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fluid_fluid_mechanics_2 - Pressure Pressure: Force per unit...

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