Unit Conversion Tables

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Appendices

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APPENDIX

A

U

nit Conversion Tables1

The following tables express the definitions of miscellaneous units of measure as exact numerical multiples of coherent SI units and provide multiplying factors for converting numbers and miscellaneous units to corresponding new numbers and SI units. Conversion factors are expressed using computer exponential notation, and an asterisk follows each number which expresses an exact definition. For example, the entry “2.54 E  2*” expresses the fact that 1 inch  2.54  102 meter, exactly by definition. Numbers not followed by an asterisk are only approximate representations of definitions or are the results of physical measurements. In these tables pound-force is designated as lbf, whereas in the text pound-force is designated as lb. ■ TA B L E

A.1 Listing by Physical Quantity To convert from

to

Multiply by

Acceleration footsecond2 free fall, standard gal (galileo) inchsecond2

metersecond2 metersecond2 metersecond2 metersecond2

3.048 E  1* 9.806 65 E  0* 1.00 E  2* 2.54 E  2*

Area acre are barn foot2

meter2 meter2 meter2 meter2

4.046 856 422 4 E  3* 1.00 E  2* 1.00 E  28* 9.290 304 E  2*

1

These Tables abridged from Mechtly, E. A., The International System of Units, 2nd Revision, NASA SP-7012, 1973.

824

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Appendix A / Unit Conversion Tables ■ ■ TA B L E

A.1

825

(continued)

To convert from

to

Multiply by

hectare inch2 mile2 (U.S. statute) section township yard2

meter2 meter2 meter2 meter2 meter2 meter2

1.00 E  4* 6.4516 E  4* 2.589 988 110 336 E  6* 2.589 988 110 336 E  6* 9.323 957 2 E  7 8.361 273 6 E  1*

Density gram centimeter3 lbminch3 lbmfoot3 slug foot3

kilogrammeter3 kilogrammeter3 kilogrammeter3 kilogrammeter3

1.00 E  3* 2.767 990 5 E  4 1.601 846 3 E  1 5.153 79 E  2

joule joule joule joule joule

1.055 056 E  3 1.054 350 E  3 4.1868 E  0 4.184 E  0* 4.1868 E  3

joule joule joule joule joule joule joule joule joule joule

4.184 E  3* 1.602 191 7 E  19 1.00 E  7* 1.355 817 9 E  0 4.214 011 0 E  2 1.000 165 E  0 4.1868 E  3 4.184 E  3* 3.60 E  6* 3.60 E  3*

Force dyne kilogram force (kgf) kilopound force kip lbf (pound force, avoirdupois) ounce force (avoirdupois) pound force, lbf (avoirdupois) poundal

newton newton newton newton newton newton newton newton

1.00 E  5* 9.806 65 E  0* 9.806 65 E  0* 4.448 221 615 260 5 E  3* 4.448 221 615 260 5 E  0* 2.780 138 5 E  1 4.448 221 615 260 5 E  0* 1.382 549 543 76 E  1*

Length angstrom astronomical unit (IAU) cubit fathom foot furlong hand inch league (international nautical) light year

meter meter meter meter meter meter meter meter meter meter

1.00 E  10* 1.496 00 E  11 4.572 E  1* 1.8288 E  0* 3.048 E  1* 2.011 68 E  2* 1.016 E  1* 2.54 E  2* 5.556 E  3* 9.460 55 E  15

Energy British thermal unit: (IST after 1956) British thermal unit (thermochemical) calorie (International Steam Table) calorie (thermochemical) calorie (kilogram, International Steam Table) calorie (kilogram, thermochemical) electron volt erg foot lbf foot poundal joule (international of 1948) kilocalorie (Internation Steam Table) kilocalorie (thermochemical) kilowatt hour watt hour

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■ Appendix A / Unit Conversion Tables ■ TA B L E

A.1

(continued)

To convert from

to

Multiply by

meter micron mil mile (U.S. statute) nautical mile (U.S.) rod yard

wavelengths Kr 86 meter meter meter meter meter meter

1.650 763 73 E  6* 1.00 E  6* 2.54 E  5* 1.609 344 E  3* 1.852 E  3* 5.0292 E  0* 9.144 E  1*

Mass carat (metric) grain gram ounce mass (avoirdupois) pound mass, lbm (avoirdupois) slug ton (long) ton (metric) ton (short, 2000 pound) tonne

kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram kilogram

2.00 E  4* 6.479 891 E  5* 1.00 E  3* 2.834 952 312 5 E  2* 4.535 923 7 E  1* 1.459 390 29 E  1 1.016 046 908 8 E  3* 1.00 E  3* 9.071 847 4 E  2* 1.00 E  3*

Power Btu (thermochemical)second calorie (thermochemical)second foot lbfsecond horsepower (550 foot lbfsecond) kilocalorie (thermochemical)second watt (international of 1948)

watt watt watt watt watt watt

1.054 350 264 488 E  3 4.184 E  0* 1.355 817 9 E  0 7.456 998 7 E  2 4.184 E  3* 1.000 165 E  0

Pressure atmosphere bar barye centimeter of mercury 10°C2 centimeter of water 14°C2 dynecentimeter2 foot of water 139.2°F2 inch of mercury 132°F2 inch of mercury 160°F2 inch of water 139.2°F2 inch of water 160°F2 kgfcentimeter2 kgfmeter2 lbffoot2 lbfinch2 (psi) millibar millimeter of mercury 10°C2 pascal psi 1lbfinch2 2 torr 10°C2

newton meter2 newton meter2 newton meter2 newtonmeter2 newton meter2 newtonmeter2 newton meter2 newton meter2 newtonmeter2 newtonmeter2 newton meter2 newton meter2 newton meter2 newton meter2 newton meter2 newton meter2 newton meter2 newtonmeter2 newton meter2 newton meter2

1.013 25 E  5* 1.00 E  5* 1.00 E  1* 1.333 22 E  3 9.806 38 E  1 1.00 E  1* 2.988 98 E  3 3.386 389 E  3 3.376 85 E  3 2.490 82 E  2 2.4884 E  2 9.806 65 E  4* 9.806 65 E  0* 4.788 025 8 E  1 6.894 757 2 E  3 1.00 E  2* 1.333 224 E  2 1.00 E  0* 6.894 757 2 E  3 1.333 22 E  2

Speed footsecond

metersecond

3.048

E  1*

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Appendix A / Unit Conversion Tables ■ ■ TA B L E

A.1

827

(continued)

To convert from

to

Multiply by

inchsecond kilometerhour knot (international) milehour (U.S. statute)

metersecond metersecond metersecond metersecond

2.54 E  2* 2.777 777 8 E  1 5.144 444 444 E  1 4.4704 E  1*

Temperature Celsius Fahrenheit Fahrenheit Rankine

kelvin kelvin Celsius kelvin

tK tK tC tK

Time day (mean solar) hour (mean solar) minute (mean solar) year (calendar)

second second second second

Viscosity centistoke stoke foot2second centipoise lbmfoot second lbf second foot2 poise poundal second foot2 slugfoot second rhe

meter2second meter2second meter2second newton second meter2 newton second meter2 newton second meter2 newton second meter2 newton second meter2 newton second meter2 meter2newton second

1.00 E  6* 1.00 E  4* 9.290 304 E  2* 1.00 E  3* 1.488 163 9 E  0 4.788 025 8 E  1 1.00 E  1* 1.488 163 9 E  0 4.788 025 8 E  1 1.00 E  1*

Volume acre foot barrel (petroleum, 42 gallons) board foot bushel (U.S.) cord cup dram (U.S. fluid) fluid ounce (U.S.) foot3 gallon (U.K. liquid) gallon (U.S. liquid) inch3 liter ounce (U.S. fluid) peck (U.S.) pint (U.S. liquid) quart (U.S. liquid) stere tablespoon teaspoon yard3

meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3 meter3

1.233 481 837 547 52 E  3* 1.589 873 E  1 2.359 737 216 E  3* 3.523 907 016 688 E  2* 3.624 556 3 E  0 2.365 882 365 E  4* 3.696 691 195 312 5 E  6* 2.957 352 956 25 E  5* 2.831 684 659 2 E  2* 4.546 087 E  3 3.785 411 784 E  3* 1.638 706 4 E  5* 1.00 E  3* 2.957 352 956 25 E  5* 8.809 767 541 72 E  3* 4.731 764 73 E  4* 9.463 529 5 E  4 1.00 E  0* 1.478 676 478 125 E  5* 4.928 921 593 75 E  6* 7.645 548 579 84 E  1*

(mean (mean (mean (mean

solar) solar) solar) solar)

 tC  273.15  15921tF  459.672  15921tF  322  1592tR

8.64 E  4* 3.60 E  3* 6.00 E  1* 3.1536 E  7*

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APPENDIX

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B

Physical Properties of Fluids

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Appendix B / Physical Properties of Fluids ■

829

4.0 2.0 1.0 8 6

Glycerin Castor oil

4 2 1 × 10–1 8 6

SAE 30W oil

4 SAE 10W-30 oil 2 SAE 10W oil

µ , Dynamic viscosity, N • s/m2

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1 × 10–2 8 6 4

Kerosine

2 Mercury 1 × 10–3 8 6

Octane

Carbon tetrachloride

Heptane

4

Water 2 1 × 10–4 8 6 4 2

Methane

Carbon dioxide

Air

Helium

1 × 10–5 8 6 –20

Hydrogen 0

20

40

60

80

100

120

Temperature, °C

■ F I G U R E B . 1 Dynamic (absolute) viscosity of common fluids as a function of temperature. To convert to BG units of lbsft2 multiply Nsm2 by 2.089  10 2. (Curves from R. W. Fox and A. T. McDonald, Introduction to Fluid Mechanics, 3rd Ed., Wiley, New York, 1985. Used by permission.)

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■ Appendix B / Physical Properties of Fluids 1 × 10–2 8 6 4

1 × 10–3 8 6

in er yc Gl oil W 30

E SA

2

SA

E

10

W

4

–3

0

oi

l Helium

2

Hydrogen

ν , Kinematic viscosity, m2/s

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1 × 10–4 8 6

SA

E

4

10

W

Methane

oil

Air

2 1 × 10–5 8 6

oxide Carbon di

4 Kero

sine

2

Wat

Octa

1 × 10–6 8 6

er

ne

Heptane

4 Carbon te trachlor

ide

2 Mercury 1 × 10–7 8 –20

0

20

40

60

80

100

120

Temperature, °C

■ F I G U R E B . 2 Kinematic viscosity of common fluids (at atmospheric pressure) as a function of temperature. To convert to BG units of ft2s multiply m2s by 10.76. (Curves from R. W. Fox and A. T. McDonald, Introduction to Fluid Mechanics, 3rd Ed., Wiley, New York, 1985. Used by permission.)

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Appendix B / Physical Properties of Fluids ■

831

■ TA B L E

B.1 Physical Properties of Water (BG Units)a

Temperature (F)

Density, R (slugsft3)

Specific Weightb, G (lbft3)

32 40 50 60 70 80 90 100 120 140 160 180 200 212

1.940 1.940 1.940 1.938 1.936 1.934 1.931 1.927 1.918 1.908 1.896 1.883 1.869 1.860

62.42 62.43 62.41 62.37 62.30 62.22 62.11 62.00 61.71 61.38 61.00 60.58 60.12 59.83

Dynamic Viscosity, M (lbsft2) 3.732 3.228 2.730 2.344 2.037 1.791 1.500 1.423 1.164 9.743 8.315 7.207 6.342 5.886

E5 E5 E5 E5 E5 E5 E5 E5 E5 E6 E6 E6 E6 E6

Kinematic Viscosity, N (ft2 s) 1.924 1.664 1.407 1.210 1.052 9.262 8.233 7.383 6.067 5.106 4.385 3.827 3.393 3.165

E5 E5 E5 E5 E5 E6 E6 E6 E6 E6 E6 E6 E6 E6

Surface Tensionc, S (lbft) 5.18 5.13 5.09 5.03 4.97 4.91 4.86 4.79 4.67 4.53 4.40 4.26 4.12 4.04

E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3

Vapor Pressure, pv [lbin2.(abs)] 8.854 1.217 1.781 2.563 3.631 5.069 6.979 9.493 1.692 2.888 4.736 7.507 1.152 1.469

E2 E1 E1 E1 E1 E1 E1 E1 E0 E0 E0 E0 E1 E1

Speed of Soundd, c (fts) 4603 4672 4748 4814 4871 4819 4960 4995 5049 5091 5101 5195 5089 5062

a

Based on data from Handbook of Chemistry and Physics, 69th Ed., CRC Press, 1988. Where necessary, values obtained by interpolation. Density and specific weight are related through the equation g  rg. For this table, g  32.174 fts2. c In contact with air. d From R. D. Blevins, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., Inc., New York, 1984. b

■ TA B L E

B.2 Physical Properties of Water (SI Units)a

Temperature (C)

Density, R (kgm3)

Specific Weightb, G (kNm3)

0 5 10 20 30 40 50 60 70 80 90 100

999.9 1000.0 999.7 998.2 995.7 992.2 988.1 983.2 977.8 971.8 965.3 958.4

9.806 9.807 9.804 9.789 9.765 9.731 9.690 9.642 9.589 9.530 9.467 9.399

a

Dynamic Viscosity, M (Ns m2) 1.787 1.519 1.307 1.002 7.975 6.529 5.468 4.665 4.042 3.547 3.147 2.818

E3 E3 E3 E3 E4 E4 E4 E4 E4 E4 E4 E4

Kinematic Viscosity, N (m2s) 1.787 1.519 1.307 1.004 8.009 6.580 5.534 4.745 4.134 3.650 3.260 2.940

E6 E6 E6 E6 E7 E7 E7 E7 E7 E7 E7 E7

Surface Tensionc, S (Nm) 7.56 7.49 7.42 7.28 7.12 6.96 6.79 6.62 6.44 6.26 6.08 5.89

Based on data from Handbook of Chemistry and Physics, 69th Ed., CRC Press, 1988. Density and specific weight are related through the equation g  rg. For this table, g  9.807 ms2. c In contact with air. d From R. D. Blevins, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., Inc., New York, 1984. b

E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2

Vapor Pressure, pv [Nm2(abs)] 6.105 8.722 1.228 2.338 4.243 7.376 1.233 1.992 3.116 4.734 7.010 1.013

E2 E2 E3 E3 E3 E3 E4 E4 E4 E4 E4 E5

Speed of Soundd, c (ms) 1403 1427 1447 1481 1507 1526 1541 1552 1555 1555 1550 1543

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■ Appendix B / Physical Properties of Fluids

■ TA B L E

B.3 Physical Properties of Air at Standard Atmospheric Pressure (BG Units)a

Temperature (F) 40 20 0 10 20 30 40 50 60 70 80 90 100 120 140 160 180 200 300 400 500 750 1000 1500 a

Density, R (slugsft3) 2.939 2.805 2.683 2.626 2.571 2.519 2.469 2.420 2.373 2.329 2.286 2.244 2.204 2.128 2.057 1.990 1.928 1.870 1.624 1.435 1.285 1.020 8.445 6.291

E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E3 E4 E4

Specific Weightb, G (lbft3) 9.456 9.026 8.633 8.449 8.273 8.104 7.942 7.786 7.636 7.492 7.353 7.219 7.090 6.846 6.617 6.404 6.204 6.016 5.224 4.616 4.135 3.280 2.717 2.024

E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2 E2

Dynamic Viscosity, M (lbsft2) 3.29 3.34 3.38 3.44 3.50 3.58 3.60 3.68 3.75 3.82 3.86 3.90 3.94 4.02 4.13 4.22 4.34 4.49 4.97 5.24 5.80 6.81 7.85 9.50

E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7

Kinematic Viscosity, N (ft2s) 1.12 1.19 1.26 1.31 1.36 1.42 1.46 1.52 1.58 1.64 1.69 1.74 1.79 1.89 2.01 2.12 2.25 2.40 3.06 3.65 4.51 6.68 9.30 1.51

E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E3

Based on data from R. D. Blevins, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., Inc., New York, 1984. Density and specific weight are related through the equation g  rg. For this table g  32.174 fts2.

b

Specific Heat Ratio, k (—)

Speed of Sound, c (fts)

1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.400 1.400 1.400 1.400 1.399 1.399 1.399 1.398 1.394 1.389 1.383 1.367 1.351 1.329

1004 1028 1051 1062 1074 1085 1096 1106 1117 1128 1138 1149 1159 1180 1200 1220 1239 1258 1348 1431 1509 1685 1839 2114

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Appendix B / Physical Properties of Fluids ■

833

■ TA B L E

B.4 Physical Properties of Air at Standard Atmospheric Pressure (SI Units)a

Temperature (C)

Density, R (kgm3)

Specific Weightb, G (Nm3)

40 20 0 5 10 15 20 25 30 40 50 60 70 80 90 100 200 300 400 500 1000

1.514 1.395 1.292 1.269 1.247 1.225 1.204 1.184 1.165 1.127 1.109 1.060 1.029 0.9996 0.9721 0.9461 0.7461 0.6159 0.5243 0.4565 0.2772

14.85 13.68 12.67 12.45 12.23 12.01 11.81 11.61 11.43 11.05 10.88 10.40 10.09 9.803 9.533 9.278 7.317 6.040 5.142 4.477 2.719

a

Dynamic Viscosity, M (Nsm2) 1.57 1.63 1.71 1.73 1.76 1.80 1.82 1.85 1.86 1.87 1.95 1.97 2.03 2.07 2.14 2.17 2.53 2.98 3.32 3.64 5.04

E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5

Kinematic Viscosity, N (m2s) 1.04 1.17 1.32 1.36 1.41 1.47 1.51 1.56 1.60 1.66 1.76 1.86 1.97 2.07 2.20 2.29 3.39 4.84 6.34 7.97 1.82

E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E4

Based on data from R. D. Blevins, Applied Fluid Dynamics Handbook, Van Nostrand Reinhold Co., Inc., New York, 1984. Density and specific weight are related through the equation g  rg. For this table g  9.807 ms2.

b

Specific Heat Ratio, k (—)

Speed of Sound, c (ms)

1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.401 1.400 1.400 1.400 1.399 1.399 1.399 1.398 1.397 1.390 1.379 1.368 1.357 1.321

306.2 319.1 331.4 334.4 337.4 340.4 343.3 346.3 349.1 354.7 360.3 365.7 371.2 376.6 381.7 386.9 434.5 476.3 514.1 548.8 694.8

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APPENDIX

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C

roperties of the U.S. P Standard Atmosphere ■ TA B L E

C.1 Properties of the U.S. Standard Atmosphere (BG Units)a

Altitude (ft)

Temperature (F)

Acceleration of Gravity, g (fts2)

5,000 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000 60,000 70,000 80,000 90,000 100,000 150,000 200,000 250,000

76.84 59.00 41.17 23.36 5.55 12.26 30.05 47.83 65.61 69.70 69.70 69.70 69.70 67.42 61.98 56.54 51.10 19.40 19.78 88.77

32.189 32.174 32.159 32.143 32.128 32.112 32.097 32.082 32.066 32.051 32.036 32.020 31.990 31.959 31.929 31.897 31.868 31.717 31.566 31.415

a

Pressure, p [lbin.2(abs)] 17.554 14.696 12.228 10.108 8.297 6.759 5.461 4.373 3.468 2.730 2.149 1.692 1.049 0.651 0.406 0.255 0.162 0.020 0.003 0.000

Density, R (slugsft3) 2.745 2.377 2.048 1.756 1.496 1.267 1.066 8.907 7.382 5.873 4.623 3.639 2.256 1.392 8.571 5.610 3.318 3.658 5.328 6.458

E3 E3 E3 E3 E3 E3 E3 E4 E4 E4 E4 E4 E4 E4 E5 E5 E5 E6 E7 E8

Data abridged from U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C.

834

Dynamic Viscosity, M (lbsft2) 3.836 3.737 3.637 3.534 3.430 3.324 3.217 3.107 2.995 2.969 2.969 2.969 2.969 2.984 3.018 3.052 3.087 3.511 3.279 2.846

E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7 E7

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Appendix C / Properties of the U.S. Standard Atmosphere ■

835

■ TA B L E

C.2 Properties of the U.S. Standard Atmosphere (SI Units)a

Altitude (m)

Temperature (C)

Acceleration of Gravity, g (ms2)

1,000 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 15,000 20,000 25,000 30,000 40,000 50,000 60,000 70,000 80,000

21.50 15.00 8.50 2.00 4.49 10.98 17.47 23.96 30.45 36.94 43.42 49.90 56.50 56.50 51.60 46.64 22.80 2.50 26.13 53.57 74.51

9.810 9.807 9.804 9.801 9.797 9.794 9.791 9.788 9.785 9.782 9.779 9.776 9.761 9.745 9.730 9.715 9.684 9.654 9.624 9.594 9.564

a

Pressure, p [Nm2(abs)] 1.139 1.013 8.988 7.950 7.012 6.166 5.405 4.722 4.111 3.565 3.080 2.650 1.211 5.529 2.549 1.197 2.871 7.978 2.196 5.221 1.052

E5 E5 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E4 E3 E3 E3 E2 E1 E1 E0 E0

Density, R (kgm3) 1.347 1.225 1.112 1.007 9.093 8.194 7.364 6.601 5.900 5.258 4.671 4.135 1.948 8.891 4.008 1.841 3.996 1.027 3.097 8.283 1.846

E0 E0 E0 E0 E1 E1 E1 E1 E1 E1 E1 E1 E1 E2 E2 E2 E3 E3 E4 E5 E5

Data abridged from U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, D.C.

Dynamic Viscosity, M (Nsm2) 1.821 1.789 1.758 1.726 1.694 1.661 1.628 1.595 1.561 1.527 1.493 1.458 1.422 1.422 1.448 1.475 1.601 1.704 1.584 1.438 1.321

E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5 E5

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APPENDIX

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D

ompressible Flow Graphs C for an Ideal Gas (k  1.4)

836

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Appendix D / Compressible Flow Graphs for an Ideal Gas (k  1.4) ■ 0.1 1.0

0.5

1.0

5.0

T __ T0

0.8

0.6

p __

7.0

6.0

A ___

p0

T __ T0

ρ __

8.0

ρ __ ρ0

0.7

p0

10.0 10.0

9.0

0.9

p __

837

A* A ___

0.5

5.0

0.4

4.0

0.3

3.0

0.2

2.0

0.1

1.0

A*

ρ0

0.0 0.1

0.5

1.0 Ma

5.0

0.0 10.0

■ F I G U R E D . 1 Isentropic flow of an ideal gas with k  1.4. (Graph provided by Professor Bruce A. Reichert of Kansas State University.)

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■ Appendix D / Compressible Flow Graphs for an Ideal Gas (k  1.4) 0.1 5.0

0.5

1.0

5.0

10.0 5.0

p ___ p0*

4.0

4.0

3.0

3.0

2.0

2.0

V ___ V*

1.0

1.0

f(l* – l) _______ D p __ p*

0.0 0.1

0.5

1.0 Ma

T __ T*

5.0

0.0 10.0

■ F I G U R E D . 2 Fanno flow of an ideal gas with k  1.4. (Graph provided by Professor Bruce A. Reichert of Kansas State University.)

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Appendix D / Compressible Flow Graphs for an Ideal Gas (k  1.4) ■ 0.1 2.5

0.5

1.0

5.0

839

10.0 2.5

p0 ____ p0,a

2.0

2.0

ρ ___

1.5

ρa

&

V ___ V*

1.5

1.0

1.0

T0 ____ T0,a 0.5

0.5

T __ Ta p __ pa 0.0 0.1

0.5

1.0 Ma

5.0

0.0 10.0

■ F I G U R E D . 3 Rayleigh flow of an ideal gas with k  1.4. (Graph provided by Professor Bruce A. Reichert of Kansas State University.)

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■ Appendix D / Compressible Flow Graphs for an Ideal Gas (k  1.4) 1.0 1.0

2.0

3.0

4.0

5.0 40.0

p0,y ____

0.8

p0,x

p0,y ____ px

30.0

p px

May

y ___

0.6

T Tx

y ___

p px

May

y ___

p p0, x

0, y _____

ρy ___ ρx

20.0

V Vy

x ___

0.4

p px

0,y ____

10.0 0.2

ρ

___y

ρx

V

&

x ___

Vy T

y ___

Tx 0.0 1.0

2.0

3.0 Max

4.0

0.0 5.0

■ F I G U R E D . 4 Normal shock flow of an ideal gas with k  1.4. (Graph provided by Professor Bruce A. Reichert of Kansas State University.)