# lecture 25 - Thermal and Fluids Engineering I Lecture 25...

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Thermal and Fluids Engineering I Lecture 25 Page 1 Lecture 25 – Review Conservation of Mass: dt dm m m system e i = ∑∑ & & Most common problems: - Students forget to use it - Often used with conservation of energy, Bernoulli, steady flow energy equation, conservation of momentum Fundamental Flow Equations: VA = & V mA ρ = & V V mV v == & & & Most common problem: Careless errors Using V for V & , saying V v m & & = etc. Check units!

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Thermal and Fluids Engineering I Lecture 25 Page 2 Manometers: Forces on Pistons: A F P = (pressure forces shown offset from center for clarity. Forces actually go through center) Most common problems: Not drawing free body diagrams and making force balance Forgetting A P atm or A P gas 1 1 1 2 gh P P ρ + = 2 2 2 3 gh P P + = 2 2 1 1 1 3 gh gh P P + + = 5 4 3 P P P = =
Thermal and Fluids Engineering I Lecture 25 Page 3 Two- phase relations: g f g m x mm = + ) ( f g f v v x v v + = ) ( f g f u u x u u + = ) ( f g f h h x h h + = Properties : Pv u h + = PV U H + = mv V = mu U = mh H = Most common problems: Knowing that v is the average for the mixture, v f is only the liquid part and v g is only the vapor part Using V instead of v or U instead of u State Principle: - two independent intensive properties determine the state Most common problem: - using T and P as properties in the 2-phase region

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Thermal and Fluids Engineering I Lecture 25 Page 4 Ideal Gas Law M T R m PV = M T R P = ν M T R P ρ = Specific Heat dT c du v = T c u v = dT c dh p = T c h p = v p c c for liquids and solids
Thermal and Fluids Engineering I Lecture 25 Page 5 Most Common Problems: units in ideal gas law confusing u and h Work: Definition x F W = Expansion or compression WP d V = (slow process) V P W = if P is constant Electrical work WI ξ = & Shaft work 2 Wn π =ℑ & & sec rev n = & Polytropic Process: C PV n = C – constant n V P V P W = 1 1 1 2 2 1 n 22 11 ln ln VV mRT V VM V == 1 n = , isothermal The First Law – Closed System: W Q U PE KE = + + 21 1 () 2 KE m ∆= z mg PE =

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Thermal and Fluids Engineering I Lecture 25 Page 6 Most Common assumptions: V is constant ( W =0) P is constant WP V =∆ Q is zero adiabatic, insulated T is constant 0 = U Isothermal The First Law –Open System: 2 2 e i () ( ) 22 cv cv cv i i i e e e dE QW m h g zm h gz dt =−+ + + + + ∑∑ & & && V V Nozzle or Diffuser Throttle 2 2 e i ie hh += + V V e i h h = Turbines Compressor 2 i 2 e 2 0 2 ii i ee e mh g z g z −+ + + + = & & & & V V 0 = + e e i h m h m W Q & & & & if insulated or ideal 0 = Q & If V < 100 s ft , 2 2 V is negligible If not hydroturbine, neglect PE one stream in and out m m m e i & & & = = Simple turbine or compressor W h h m e i & & = ) (
Thermal and Fluids Engineering I Lecture 25 Page 7 Mixing Chamber (insulated) e e i i h m h m = & & = e e i i m m & & Pump Heat Exchanger (insulated) ) ( i e i e P P v h h = e e i i h m h m = & & ) ( e i P P v m W = & & Forces on Submerged Surface A y g A P F c atm R θ ρ

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lecture 25 - Thermal and Fluids Engineering I Lecture 25...

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