APPENDIX A. Summary of the English Engineering (EE) System of Units
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1 Appendixes A. Summary of the English Engineering (EE) System of Units B. Summary of the International System (SI) of Units C. Friction-Factor Chart D. Oblique-Shock Charts (γ = 1.4) (Two-Dimensional) E. Conical-Shock Charts (γ = 1.4) (Three-Dimensional) F. Generalized Compressibility Factor Chart G. Isentropic Flow Parameters (γ = 1.4) (including Prandtl Meyer Function) H. Normal-Shock Parameters (γ = 1.4) I. Fanno Flow Parameters (γ = 1.4) J. Rayleigh Flow Parameters (γ = 1.4) K. Properties of Air at Low Pressures L. 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 397 Force pound force lbf Mass pound mass lbm Length foot ft Time second sec Temperature Rankine 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/second 2. Thus F = ma g c 1(lbf) = 1 (lbm) (ft/sec2 ) g c g c = lbm-ft/lbf-sec 2 Temperature T( R) = T( F) Gas constant R = 1545/M.M. * ft-lbf/1bm- R Pressure 1 atm = lbf/ft 2 Heat to work 1 Btu = ft-lbf Power 1 hp = 550 ft-lbf/sec Standard gravity g 0 = ft/sec 2 * M.M., molecular mass.
4 398 APPENDIX A Useful Conversion Factors To convert from: To: Multiply by: meter foot meter inch newton lbf kilogram lbm K R joule (q) Btu kwh (q) Btu joule (w) ft-lbf watt horsepower m/s (V) ft/sec m/s (V) mph km/h (V) mph N/m 2 (p) atmosphere N/m 2 (p) lbf/in N/m 2 (p) lbf/ft kg/m 3 (ρ) lbm/ft N s/m 2 (μ) lbf-sec/ft m 2 /s (ν) ft 2 /sec J/kg K (c p ) Btu/lbm- R N m/kg K (R) ft-lbf/lbm- R Source: The International System of Units, NASA SP-7012, 1973.
5 Properties of Gases English Engineering (EE) System a Gas Constant Specific Heats Viscosity Critical Point Molecular γ = c p R Btu/lbm- R μ Tc pc Gas Symbol Mass ft-lbf/lbm- R cp cv lbf-sec/ft 2 R psia cv Air Argon Ar Carbon dioxide CO Carbon monoxide CO Helium He Hydrogen H Methane CH Nitrogen N Oxygen O Water vapor H2O a Values for γ, R, c p, cv, and μ are for normal room temperature and pressure. 399
6 APPENDIX B Summary of the International System (SI) of Units 400
7 SUMMARY OF THE INTERNATIONAL SYSTEM (SI) OF UNITS 401 Force newton N Mass kilogram kg Length meter m Time second s Temperature kelvin K A 1-Newton force will give a 1-kilogram mass an acceleration of 1 meter/second 2. Thus F = ma g c 1(N) = 1 (kg) 1 (m/s2 ) g c g c = 1kg m/n s 2 Temperature T(K) = T( C) Gas constant R = 8314/M.M. * N m/kg K Pressure 1 atm = N/m 2 1 pascal (Pa) = 1 N/m 2 1 bar (bar) = N/m 2 1MPa = N/m 2 Heat to work 1 joule (J) = 1N m Power 1 watt (W) = 1 J/s Standard gravity g 0 = 9.81 m/s 2 * M.M., molecular mass.
8 402 APPENDIX B Useful Conversion Factors To convert from: To: Multiply by: foot meter inch meter lbf newton lbm kilogram R K Btu (q) joule Btu (q) kwh ft-lbf (w) joule horsepower watt ft/sec (V) m/s mph (V) m/s mph (V) km/h atmosphere (p) N/m lbf/in 2 (p) N/m lbf/ft 2 (p) N/m lbm/ft 3 (ρ) kg/m lbf-sec/ft 2 (μ) N s/m ft 2 /sec (ν) m 2 /s Btu/lbm- R (c p ) J/kg K ft-lbf/lbm- R (R) N m/kg K Source: The International System of Units, NASA SP-7012, 1973.
9 Properties of Gases International System (SI) a Gas Constant Specific Heats Viscosity Critical Point Molecular γ = c p R J/kg K μ Tc pc Gas Symbol Mass N m/kg K cp cv N s/m 2 K MPa cv Air , Argon Ar Carbon dioxide CO Carbon monoxide CO , Helium He ,080 5,230 3, Hydrogen H ,120 14,300 10, Methane CH ,230 1, Nitrogen N , Oxygen O Water vapor H2O ,860 1, a Values for γ, R, c p, cv, and μ are for normal room temperature and pressure. 403
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 M 1 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 M 2 for an oblique-shock wave as a function of the initial Mach number M 1 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 p 2 /p 1 across an oblique-shock wave as a function of the initial Mach number M 1 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 θ c for a conical-shock wave as a function of the initial Mach number M 1 for different values of the cone angle δ c 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 M s for a conical-shock wave as a function of the initial Mach number M 1 for different values of the cone angle δ c 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 p s /p 1 for a conical-shock wave as a function of the initial Mach number M 1 for different values of the cone angle δ c 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 (Z c = 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) 417 M p/p t T/T t A/A pa/p t A ν μ
24 418 APPENDIX G M p/p t T/T t A/A pa/p t A ν μ
25 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) 419 M p/p t T/T t A/A pa/p t A ν μ
26 420 APPENDIX G M p/p t T/T t A/A pa/p t A ν μ
27 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) 421 M p/p t T/T t A/A pa/p t A ν μ
28 422 APPENDIX G M p/p t T/T t A/A pa/p t A ν μ
29 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) 423 M p/p t T/T t A/A pa/p t A ν μ
30 424 APPENDIX G M p/p t T/T t A/A pa/p t A ν μ
31 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) 425 M p/p t T/T t A/A pa/p t A ν μ
32 426 APPENDIX G M p/p t T/T t A/A pa/p t A ν μ
33 ISENTROPIC FLOW PARAMETERS (γ = 1.4) (INCLUDING PRANDTL MEYER FUNCTION) 427 M p/p t T/T t A/A pa/p t A ν μ
34 APPENDIX H Normal-Shock Parameters (γ = 1.4) 428
35 NORMAL-SHOCK PARAMETERS (γ = 1.4) 429 M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
36 430 APPENDIX H M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
37 NORMAL-SHOCK PARAMETERS (γ = 1.4) 431 M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
38 432 APPENDIX H M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
39 NORMAL-SHOCK PARAMETERS (γ = 1.4) 433 M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
40 434 APPENDIX H M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
41 NORMAL-SHOCK PARAMETERS (γ = 1.4) 435 M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
42 436 APPENDIX H M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
43 NORMAL-SHOCK PARAMETERS (γ = 1.4) 437 M 1 M 2 p 2 /p 1 T 2 /T 1 V /a 1 p t2 /p t1 p t2 /p 1
44 APPENDIX I Fanno Flow Parameters (γ = 1.4) 438
45 FANNO FLOW PARAMETERS (γ = 1.4) 439 M T/T p/p p t /p t V/V fl max /D S max /R
46 440 APPENDIX I M T/T p/p p t /p t V/V fl max /D S max /R
47 FANNO FLOW PARAMETERS (γ = 1.4) 441 M T/T p/p p t /p t V/V fl max /D S max /R
48 442 APPENDIX I M T/T p/p p t /p t V/V fl max /D S max /R
49 FANNO FLOW PARAMETERS (γ = 1.4) 443 M T/T p/p p t /p t V/V fl max /D S max /R
50 444 APPENDIX I M T/T p/p p t /p t V/V fl max /D S max /R
51 FANNO FLOW PARAMETERS (γ = 1.4) 445 M T/T p/p p t /p t V/V fl max /D S max /R
52 446 APPENDIX I M T/T p/p p t /p t V/V fl max /D S max /R
53 FANNO FLOW PARAMETERS (γ = 1.4) 447 M T/T p/p p t /p t V/V fl max /D S max /R
54 448 APPENDIX I M T/T p/p p t /p t V/V fl max /D S max /R
55 FANNO FLOW PARAMETERS (γ = 1.4) 449 M T/T p/p p t /p t V/V fl max /D S max /R
56 APPENDIX J Rayleigh Flow Parameters (γ = 1.4) 450
57 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 451 M T t /T t T/T p/p p t /p t V/V S max /R
58 452 APPENDIX J M T t /T t T/T p/p p t /p t V/V S max /R
59 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 453 M T t /T t T/T p/p p t /p t V/V S max /R
60 454 APPENDIX J M T t /T t T/T p/p p t /p t V/V S max /R
61 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 455 M T t /T t T/T p/p p t /p t V/V S max /R
62 456 APPENDIX J M T t /T t T/T p/p p t /p t V/V S max /R
63 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 457 M T t /T t T/T p/p p t /p t V/V S max /R
64 458 APPENDIX J M T t /T t T/T p/p p t /p t V/V S max /R
65 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 459 M T t /T t T/T p/p p t /p t V/V S max /R
66 460 APPENDIX J M T t /T t T/T p/p p t /p t V/V S max /R
67 RAYLEIGH FLOW PARAMETERS (γ = 1.4) 461 M T t /T t T/T p/p p t /p t V/V S max /R
68 APPENDIX K Properties of Air at Low Pressures 462
69 PROPERTIES OF AIR AT LOW PRESSURES 463 Thermodynamic Properties of Air at Low Pressures This information is presented in English Engineering (EE) units T is in R, φ is in Btu/lbm- R. t is in F, h and u are in Btu/lbm. p r and v r are relative pressure and relative volume. T t h p r u v r φ T t h p r u v r φ
70 464 APPENDIX K Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ
71 PROPERTIES OF AIR AT LOW PRESSURES 465 Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ
72 466 APPENDIX K Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ
73 PROPERTIES OF AIR AT LOW PRESSURES 467 Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ
74 468 APPENDIX K Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ
75 PROPERTIES OF AIR AT LOW PRESSURES 469 Thermodynamic Properties of Air at Low Pressures (cont.) T t h p r u v r φ T t h p r u v r φ Source: Condensed with permission from Table 1 of J. H. Keenan and J. Kaye, Gas Tables, copyright 1948, John Wiley & Sons, New York.
76 APPENDIX L Specific Heats of Air at Low Pressures 470
77 SPECIFIC HEATS OF AIR AT LOW PRESSURES 471 Specific Heats of Air at Low Pressures This information is presented in English Engineering (EE) units. T is in R, c p is in Btu/lbm- R. t is in F, c v is in Btu/lbm- R. a is in ft/sec, γ = c p /c v. T t c p c v γ a T t c p c v γ a Source: Adapted with permission from Table 2 of J. H. Keenan and J. Kaye, Gas Tables, copyright 1948, John Wiley & Sons, New York.
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