basic_law_finite_lecture_4

basic_law_finite_lecture_4 - First Law of Thermodyamics...

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Unformatted text preview: First Law of Thermodyamics dis? 2 d9 + dW For a moving system: %E- z + W Q : heat transfer rate to the system W =rate of work clone on the system 3 = e + V2 t2 + gs = energy per unit mass E = jsa’m = Ispd‘v’ = energy in system B = [W where [3 = property per unit volume ThenB=E and t3 =pe=p(e+V2t2+gz). Work: dW = Fsds for foroe F's in the direction .533 . «it? = Fst = (FoosElMs = F—d" thdt=W=F-d§tdt:fihy Gravity: WP: = —ga'm(e'2 m 21): (potential) e (potenttoth Potential energy = gza'm and g2: potential per unit mass Werk: Pressure: d1?” p = —p¢£/iii dW=an-fi=-pI7-aaa Fer the whale system surface WP : — [pl/7 - fidA Sheer stress : dfif 2 fdA tangent to the surface element (224 as; fist—174m)? and a; : Jami WT =0: 19:0 ferasclid surface e-rze fox-es? or files Neglect fricticn wcrk. There can be fricticn work in the flew, but net on the CS. Shaft Werk: W3 = wcrk dcne by a shaft or arm sticking thrcugh the centre] surface and delivering wcrk‘ tn the CV. Reynolds transpcrt thecren : {IE 2 13— I W + H317 - rid-t Q+W=£xa Jepa’tfnr [apt/7am D: a: CV (33 H? = W5 — J‘pV-r’idAéWs — f(pfp)pI7-fidA Q+e=9 team J(8+£)pF-fid4 p 5‘ CV cs where s =e+V2f2+gz Steady flew thrcngh a devise with one entrance and an exit = I(e+f—+gz+£)pndl4~ I(e+— w+gz+—)padA A2 2 P A] 2 .0 Prcfile facter: A : (ja3dAfl H314 where E = (fad/{fl A Gravity term: [zadA = zcfiA where ac distance tc centrcid Fcr gases neglect the gravity term Unif'crm prcpertiee and velccity ever the crcsa secticn Q + It»; = auhg + V22 f2) w (a, + V12 :2)] _ h : e+pfp = enthalpy, and rt: 2 prlA] : p2V2A2 Incompressible Flow Q 2 CI: No forced heat transfer Little frictional effects Internal energy e = constant One dimensional flow at entrance and exit _ I V2 V2 mmmfl+iofiréhieem p 2 p 2 Dimensions: ~ N - m!“ s w wort dWs P2 V22 Pt V12 : —+-—+ z — —+—+ 2 dm p 2 g 2) ( 2 31) Flow in a Stream Tube 6124 /" With no shaft work ‘we obtain Bernouiii’s equation V2 V2 (%+§+en4%+g+an The sum of the pressure potential, kinetic energy and gravitational potential is constant along a flowr stream for frictionless flow. Example: Determine the Power frem the Pump Flew rate of water 4 = 0.095m3 is. Diameter ef pipe = d2 =10em Diameter ef nezzle exit = {13 = 6cm and p3 = pa p V2 p V2 as :m[(—3-+i+sza)-(-l+—2~+gzz)] p 2 p 2 ‘ _ V2_V2 me??? P“ +3—i+g<zrzz)i p 2 V2 =QI'EIA2 and V3 "—“ Pressure p2 determined fi‘em Berneulli’s equatien p1 is atmespherie and V12 «.2: V22 p2 — pa. = p[—V22 £2 + g(sl - 22)] = gas—12.1232 + 93(5)] : ~—24,060Pa — 24060 + (33.6)2 —(12.1)2 998 2 + (9.32)(3)] = 105.2%» a; : (998)({}.095)[— Solution eptien: Use Bernenlli equation to eliminate p2 - pa ...
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basic_law_finite_lecture_4 - First Law of Thermodyamics...

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