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Units and Key Constants

Units and Key Constants. Conventional Units Parameter English Units SI Units Distance Feet, Inches Meters, M Time Seconds Seconds, s Force Pounds (force), lbf 4.448 Newton, N Pressure psf, psi Pascal, Pa (1N/1m 2 ) bar (10 5 Pa) 1 ft H 2 O 2.989 kPa

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Units and Key Constants

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  1. Units and Key Constants

  2. Conventional Units ParameterEnglish UnitsSI Units • Distance Feet, Inches Meters, M • Time Seconds Seconds, s • Force Pounds (force), lbf 4.448 Newton, N • Pressure psf, psi Pascal, Pa (1N/1m2) bar (105Pa) 1 ft H2O 2.989 kPa • Mass Pounds (mass), lbm 0.4536 kilogram • Energy Btu Joule, J • Power 1 Hp 0.7457 kWatt

  3. Equivalent Systems of Units

  4. Important Constants for Air

  5. Useful Equivalents

  6. For Liquid Water : • U.S. Standard Atmosphere - 1976

  7. Standard Atmosphere Altitude Stratosphere >65,000 ft Altitude 36,089 ft 3.202 psia 36,089 ft 14.696 psia 59 F Pressure Temperature

  8. Thermodynamics Review

  9. Thermodynamics Review • Thermodynamic views • microscopic: collection of particles in random motion. Equilibrium refers to maximum state of disorder • macroscopic: gas as a continuum. Equilibrium is evidenced by no gradients • 0th Law of Thermo [thermodynamic definition of temperature]: • When any two bodies are in thermal equilibrium with a third, they are also in thermal equilibrium with each other. • Correspondingly, when two bodies are in thermal equilibrium with one another they are said to be at the same temperature.

  10. Thermodynamics Review • 1st Law of Thermo [Conservation of energy]: Total work is same in all adiabatic processes between any two equilibrium states having same kinetic and potential energy. • Introduces idea of stored or internal energy E • dE = dQ - dW • dW = Work done by system [+]=dWout= - pdV • Some books have dE=dQ+dW [where dW is work done ON system] • dQ = Heat added to system [+]=dQin • Heat and work are mutually convertible. Ratio of conversion is called mechanical equivalent of heat J = joule

  11. Review of Thermodynamics • Stored energy E components • Internal energy (U), kinetic energy (mV2/2), potential energy, chemical energy • Energy definitions • Introduces e = internal energy = e(T, p) • e = e(T)  de = Cv(T) dT thermally perfect • e = Cv T calorically perfect • 2nd law of Thermo • Introduces idea of entropy S • Production of s must be positive • Every natural system, if left undisturbed, will change spontaneously and approach a state of equilibrium or rest. The property associated with the capability of systems for change is called entropy.

  12. Review of Thermodynamics • Extensive variables – depend on total mass of the system, e.g. M, E, S, V • Intensive variables – do not depend on total mass of the system, e.g. p, T, s,  (1/v) • Equilibrium (state of maximum disorder) – bodies that are at the same temperature are called in thermal equilibrium. • Reversible – process from one state to another state during which the whole process is in equilibrium • Irreversible – all natural or spontaneous processes are irreversible, e.g. effects of viscosity, conduction, etc.

  13. Thermodynamic Properties Derived Primitive

  14. 1st Law of Thermodynamics • For steady flow, defining: • We can write: • and

  15. 1st Law of Thermodynamics • Substituting back into 1st law: • Height term often negligible (not for hydraulic machines) • Defining total or stagnation enthalpy: • The first law for open systems is:

  16. Equation of State • The relation between the thermodynamic properties of a pure substance is referred to as the equation of state for that substance, i.e. F(p, v, T) = 0 • Ideal (Perfect) Gas • Intermolecular forces are neglected • The ratio pV/T in limit as p  0 is known as the universal gas constant (R). p  /T  R = 8.3143e3 • At sufficiently low pressures, for all gases p/T = R or • Real gas: intermolecular forces are important

  17. Real Gas

  18. Real Gas

  19. 1st & 2nd Law of Thermodynamics • Gibbs Eqn. relates 2nd law properties to 1st law properties:

  20. Gibbs Equation • Isentropic form of Gibbs equation: • and using specific heat at constant pressure:

  21. Thermally & Calorically Perfect Gas • Also, for a thermally perfect gas Cp[T]: • Calorically perfect gas - Constant Cp

  22. Isentropic Flow • For Isentropic Flow [if dQ=0, Adiabatic Gas Law]: • Precise gas tables available for design work • Thermally Perfect Gas good flows at moderate temperature.

  23. Common Gases monatomic diatomic polyatomic

  24. Important Constants for Air

  25. Gibbs Equation • Rewriting Gibbs Equation:

  26. Gibbs Equation • Rewriting Gibbs Equation:

  27. Isobars are not parallel

  28. Mollier for Static / Total States Poout h02 h02i We will soon see V2/2 Poin h01 s

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