Mechanical Engineering Department Third year class Gas Dynamics Tables Lecturer: Dr.Naseer Al-Janabi

Transcription

1 Mechanical Engineering Department Third year class Gas Dynamics Tables Lecturer: Dr.Naseer Al-Janabi Ref. Fundamentals of Gas Dynamics, 2e - R. Zucker, O. Biblarz Appendixes A. B. C. D. E. F. G. H. I. J. K. L. Summary of the English Engineering (EE) System of Units Summary of the International System (SI) of Units Friction-Factor Chart Oblique-Shock Charts (γ = 1.4) (Two-Dimensional) Conical-Shock Charts (γ = 1.4) (Three-Dimensional) Generalized Compressibility Factor Chart Isentropic Flow Parameters (γ = 1.4) (including Prandtl Meyer Function) Normal-Shock Parameters (γ = 1.4) Fanno Flow Parameters (γ = 1.4) Rayleigh Flow Parameters (γ = 1.4) Properties of Air at Low Pressures Specific Heats of Air at Low Pressures 395

2 APPENDIX A Summary of the English Engineering (EE) System of Units 396

3 SUMMARY OF THE ENGLISH ENGINEERING (EE) SYSTEM OF UNITS Force Mass Length Time Temperature pound force pound mass foot second Rankine lbf lbm ft sec R NEVER say pound, as this is ambiguous! It is either a pound force (lbf) or a pound mass (lbm). A 1-pound force will give a 1-pound mass an acceleration of feet/second2. F = 1(lbf) = ma gc 1 (lbm) (ft/sec2 ) gc Thus gc = lbm-ft/lbf-sec2 Temperature Gas constant Pressure Heat to work Power Standard gravity * M.M., molecular mass. T ( R) R 1 atm 1 Btu 1 hp g0 = = = = = = T ( F) /M.M.* ft-lbf/1bm- R lbf/ft ft-lbf 550 ft-lbf/sec ft/sec2 397

4 398 APPENDIX A Useful Conversion Factors To convert from: To: Multiply by: meter meter newton kilogram K joule kwh joule watt m/s m/s km/h N/m2 N/m2 N/m2 kg/m3 N s/m2 m2/s J/kg K N m/kg K foot inch lbf lbm R Btu Btu ft-lbf horsepower ft/sec mph mph atmosphere lbf/in2 lbf/ft2 lbm/ft3 lbf-sec/ft2 ft2/sec Btu/lbm- R ft-lbf/lbm- R (q) (q) (w) (V ) (V ) (V ) (p) (p) (p) (ρ) (µ) (ν) (cp ) (R) Source: The International System of Units, NASA SP-7012, 1973.

5 399 a Ar CO2 CO He H2 CH4 N2 O2 H2O Argon Carbon dioxide Carbon monoxide Helium Hydrogen Methane Nitrogen Oxygen Water vapor cp γ = cv Gas Constant R ft-lbf/lbm- R Values for γ, R, cp, cv, and µ are for normal room temperature and pressure Symbol Air Gas Molecular Mass Properties of Gases English Engineering (EE) System a Specific Heats Btu/lbm- R cp cv Critical Point Tc pc R psia Viscosity µ lbf-sec/ft2

6 APPENDIX B Summary of the International System (SI) of Units 400

7 SUMMARY OF THE INTERNATIONAL SYSTEM (SI) OF UNITS Force Mass Length Time Temperature newton kilogram meter second kelvin N kg m s K A 1-Newton force will give a 1-kilogram mass an acceleration of 1 meter/second2. F = 1(N) = ma gc 1 (kg) 1 (m/s2 ) gc Thus gc = 1 kg m/n s2 Temperature Gas constant Pressure Heat to work Power Standard gravity * M.M., molecular mass. T (K) R 1 atm 1 pascal (Pa) 1 bar (bar) 1 MPa 1 joule (J) 1 watt (W) g0 = = = = = = = = = T ( C) /M.M.* N m/kg K N/m2 1 N/m N/m N/m2 1N m 1 J/s 9.81 m/s2 401

8 402 APPENDIX B Useful Conversion Factors To convert from: To: Multiply by: foot inch lbf lbm R Btu Btu ft-lbf horsepower ft/sec mph mph atmosphere lbf/in2 lbf/ft2 lbm/ft3 lbf-sec/ft2 ft2/sec Btu/lbm- R ft-lbf/lbm- R meter meter newton kilogram K joule kwh joule watt m/s m/s km/h N/m2 N/m2 N/m2 kg/m3 N s/m2 m2/s J/kg K N m/kg K (q) (q) (w) (V ) (V ) (V ) (p) (p) (p) (ρ) (µ) (ν) (cp ) (R) Source: The International System of Units, NASA SP-7012, 1973.

9 403 a Ar CO2 CO He H2 CH4 N2 O2 H2O Argon Carbon dioxide Carbon monoxide Helium Hydrogen Methane Nitrogen Oxygen Water vapor cp γ = cv ,120 2, Gas Constant R N m/kg K Values for γ, R, cp, cv, and µ are for normal room temperature and pressure Symbol Air Gas Molecular Mass Properties of Gases International System (SI) a 1, ,040 2,230 14,300 5,230 1, ,000 1, ,690 10,200 3, Specific Heats J/kg K cp cv Critical Point Tc pc K MPa Viscosity µ N s/m2

10 APPENDIX C Friction-Factor Chart 404

11 405 Figure AC.1 Moody diagram for determination of friction factor. (Adapted with permission from L. F. Moody, Friction factors for pipe flow, Transactions of ASME, Vol. 66, 1944.)

12 APPENDIX D Oblique-Shock Charts (γ = 1.4) (Two-Dimensional) 406

13 OBLIQUE-SHOCK CHARTS (γ = 1.4) 407 Figure AD.1 Shock-wave angle θ as a function of the initial Mach number M1 for different values of the flow deflection angle δ for γ = 1.4. (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

14 408 APPENDIX D Figure AD.2 Mach number downstream M2 for an oblique-shock wave as a function of the initial Mach number M1 for different values of the flow deflection angle δ for γ = 1.4. (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

15 OBLIQUE-SHOCK CHARTS (γ = 1.4) 409 Figure AD.3 Static pressure ratio p2 /p1 across an oblique-shock wave as a function of the initial Mach number M1 for different values of the flow deflection angle δ for γ = (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

16 APPENDIX E Conical-Shock Charts (γ = 1.4) (Three-Dimensional) at 410

17 CONICAL-SHOCK CHARTS (γ = 1.4) 411 c c Figure AE.1 Shock wave angle θc for a conical-shock wave as a function of the initial Mach number M1 for different values of the cone angle δc for γ = (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

18 412 APPENDIX E c Figure AE.2 Surface Mach number Ms for a conical-shock wave as a function of the initial Mach number M1 for different values of the cone angle δc for γ = (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

19 CONICAL-SHOCK CHARTS (γ = 1.4) 413 c Figure AE.3 Surface static pressure ratio ps /p1 for a conical-shock wave as a function of the initial Mach number M1 for different values of the cone angle δc for γ = (Adapted with permission from M. J. Zucrow and J. D. Hoffman, Gas Dynamics, Vol. I, copyright 1976, John Wiley & Sons, New York.)

20 APPENDIX F Generalized Compressibility Factor Chart 414

21 GENERALIZED COMPRESSIBILITY FACTOR CHART 415 Figure AF.1 Generalized compressibility factors (Zc = 0.27). (With permission from R. E. Sontag, C. Borgnakke, and C. J. Van Wylen, Fundamentals of Thermodynamics, 5th ed., copyright 1997, John Wiley & Sons, New York.)

22 APPENDIX G Isentropic Flow Parameters (γ = 1.4) (including Prandtl Meyer Function) 416

23 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 417 µ

24 418 M APPENDIX G p/pt T /Tt A/A pa/pt A ν µ

25 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 419 µ

26 420 M APPENDIX G p/pt T /Tt A/A pa/pt A ν µ

27 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 421 µ

28 422 M APPENDIX G p/pt T /Tt A/A pa/pt A ν µ

29 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 423 µ

30 424 M APPENDIX G p/pt T /Tt A/A pa/pt A ν µ

31 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 425 µ

32 426 M APPENDIX G p/pt T /Tt A/A pa/pt A ν µ

33 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) M p/pt T /Tt A/A pa/pt A ν 427 µ

34 APPENDIX H Normal-Shock Parameters (γ = 1.4) 428

35 NORMAL-SHOCK PARAMETERS (γ = 1.4) M1 M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 429 pt2 /p1

36 430 M1 APPENDIX H M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 pt2 /p1

37 NORMAL-SHOCK PARAMETERS (γ = 1.4) M1 M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 431 pt2 /p1

38 432 M1 APPENDIX H M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 pt2 /p1

39 NORMAL-SHOCK PARAMETERS (γ = 1.4) M1 M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 433 pt2 /p1

40 434 M1 APPENDIX H M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 pt2 /p1

41 NORMAL-SHOCK PARAMETERS (γ = 1.4) M1 M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 435 pt2 /p1

42 436 M1 APPENDIX H M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 pt2 /p1

43 NORMAL-SHOCK PARAMETERS (γ = 1.4) M1 M2 p2 /p1 T2 /T1 7V /a1 pt2 /pt1 437 pt2 /p1

44 APPENDIX I Fanno Flow Parameters (γ = 1.4) 438

45 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 439 Smax /R

46 440 M APPENDIX I T /T p/p pt /pt V /V f Lmax /D Smax /R

47 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 441 Smax /R

48 442 M APPENDIX I T /T p/p pt /pt V /V f Lmax /D Smax /R

49 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 443 Smax /R

50 444 M APPENDIX I T /T p/p pt /pt V /V f Lmax /D Smax /R

51 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 445 Smax /R

52 446 M APPENDIX I T /T p/p pt /pt V /V f Lmax /D Smax /R

53 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 447 Smax /R

54 448 M APPENDIX I T /T p/p pt /pt V /V f Lmax /D Smax /R

55 FANNO FLOW PARAMETERS (γ = 1.4) M T /T p/p pt /pt V /V f Lmax /D 449 Smax /R

56 APPENDIX J Rayleigh Flow Parameters (γ = 1.4) 450

57 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 451 Smax /R

58 452 APPENDIX J M Tt /Tt T /T p/p pt /pt V /V Smax /R

59 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 453 Smax /R

60 454 APPENDIX J M Tt /Tt T /T p/p pt /pt V /V Smax /R

61 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 455 Smax /R

62 456 APPENDIX J M Tt /Tt T /T p/p pt /pt V /V Smax /R

63 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 457 Smax /R

64 458 APPENDIX J M Tt /Tt T /T p/p pt /pt V /V Smax /R

65 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 459 Smax /R

66 460 APPENDIX J M Tt /Tt T /T p/p pt /pt V /V Smax /R

67 RAYLEIGH FLOW PARAMETERS (γ = 1.4) M Tt /Tt T /T p/p pt /pt V /V 461 Smax /R