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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 = 287Nm/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
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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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 Spring '09

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