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tf2summary2 - Thermal Fluids 2 Summary Sheet Formula KE =...

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May 8, 2009 Thermal & Fluids 2 Summary Sheet Carl Hansen Types of Energy : Static Energies: Formula Dynamic Energies Formula Kinetic Energy KE = ½m* v 2 Work w = ∫ F∙dx w = ∫ P*d V Gravitational Potential Energy GPE = m*g*h Heat Transfer Q = m*C*ΔT Strain Energy SPE = ½k*x 2 Electrical power dw/dt = i*V Internal Thermal Energy ΔU = m*C*ΔT Chemical & Nuclear Energy 1 st law of Thermodynamics: ΔE = Q – w “increase in system energy = heat added – work done by system.” ΔE = Δ(U + PE + KE) Model: heat engine system Gases: Ideal Gas law: P*V = m* K M R T * ° ; where M is molar mass, R = 8.31434 kJ/(kmol * °K) = 0.08205 K * mol atm * L ° Expansion Work: w = ∫ P*d V M air = 28.95 kJ/(kmol*°K) Special Cases: Constant Volume (d V /dt = 0): w = 0 Constant Pressure (dP/dt = 0): w = P( V 1 V 2 ) Isothermal (dT/dt = 0, or P* V =const): w = P 1 * V 1 * ( 29 1 2 V V ln Polytrophic (P* V n =const): Adiabatic(no heat transfer): n 1 V * P V * P w 1 1 2 2 - - = n = k = C p /C v k air = 1.4 More for Adiabatic, Quasi-Eqlbrm, Ideal gas, constant specific heat ( 29 k V V P P 2 1 1 2 = ( 29 1 k V V T T 2 1 1 2 - = ( 29 k 1 k P P T T 1 2 1 2 - = Specific Heats of ideal gases: c p : if it has constant pressure c v : if it has constant volume Relation: c p = c v + M R Fluid Dynamics: (a) Conservation of mass: volumetric flow rate definition: A * v V avg a = 2 2 2 1 1 1 A * v * A * v * a a ρ = ρ (b) Conservation of energy: Bernoulli Equation: 2 2 2 2 1 2 1 1 z * g 2 v P z * g 2 v P + + ρ = + + ρ (isothermal, incompressible, frictionless, zero work, adiabatic) For general open energy system: + + - + + + - = out o 2 o o o in i 2 i i i out , cv in , cv cv gz 2 v h m gz 2 v h m W Q E (c) Conservation of momentum: - + = in in in out exit exit cv v * m v * m dt B d F a Two Phase Properties: Quality of a gas/liquid mixture: L g L g L g V V V V m m m x - - + = = Specific volume: v = v L + x *(v g – v L ) = v L + x*v gL Specific Internal Energy: u = u L + x*(u g – u L ) = uL + x*u gL Specific Enthlapy: h = h L + (h g – h L )*x = h L + x*h gL Subscripts labeled “ gL ” = latent heat of vaporization.

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tf2summary2 - Thermal Fluids 2 Summary Sheet Formula KE =...

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