65:
1524:
268:
2970:
1595:
72:
There are two equations for computing pressure as a function of height. The first equation is applicable to the atmospheric layers in which the temperature is assumed to vary with altitude at a non null
2733:
2832:
2593:
1714:
3042:
397:
2641:
2876:
1366:
2075:
2044:
1965:
1930:
1741:
766:
727:
501:
462:
2249:
1879:
1846:
1770:
1354:
907:
860:
820:
692:
628:
595:
555:
427:
102:
2099:
2013:
1989:
2661:
1901:
1817:
1792:
933:
791:
654:
526:
2881:
1533:
107:
2666:
2747:
2109:
ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. The reference value for
1318:
The expressions for calculating density are nearly identical to calculating pressure. The only difference is the exponent in
Equation 1.
943:
ranges from 0 to 6 in accordance with each of seven successive layers of the atmosphere shown in the table below. In these equations,
1321:
There are two equations for computing density as a function of height. The first equation is applicable to the standard model of the
1795:
769:
504:
2550:
1602:
2977:
270:
The second equation is applicable to the atmospheric layers in which the temperature is assumed not to vary with altitude (
3172:
277:
3108:
2604:
3167:
2142:= 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when
1033:= 6 are obtained from the application of the appropriate member of the pair equations 1 and 2 for the case when
2206:
989:
3149:
1849:
863:
598:
3098:
2598:
59:
1313:
3073:(For exact results, it should be remembered that atmospheres containing water do not behave as an
3133:. NASA SP-7012, Second Revision, National Aeronautics and Space Administration, Washington, D.C.
2839:
2878:
and constant molar mass and gravitational acceleration, we get the first barometric formula:
2051:
2020:
1941:
1913:
1724:
996:
in particular does not agree with standard values for this constant. The reference value for
738:
699:
473:
434:
910:
631:
2234:
1857:
1824:
1748:
1332:
885:
838:
798:
670:
606:
573:
533:
405:
80:
2974:
Instead, assuming constant temperature, integrating gives the second barometric formula:
2082:
1996:
1972:
3152:, 1976, U.S. Government Printing Office, Washington, D.C., 1976. (Linked file is 17 Mb)
2646:
1886:
1802:
1777:
918:
776:
661:
639:
511:
1907:
or, converted to U.S. gravitational foot-pound-second units (no longer used in U.K.):
3161:
2544:
1015:
17:
3063:
3051:
2190:
are multi-valued constants in accordance with the table below. The values used for
1357:
973:
are multivalued constants in accordance with the table below. The values used for
1528:
which is equivalent to the ratio of the relative pressure and temperature changes
1519:{\displaystyle \rho =\rho _{b}\left^{\left({\frac {g_{0}M}{R^{*}L_{b}}}-1\right)}}
3103:
3082:
3067:
1933:
1322:
867:
1326:
271:
74:
3131:
The
International System of Units, Physical Constants and Conversion Factors
64:
3078:
2737:
47:
39:
43:
35:
2213:
in particular does not agree with standard values for this constant.
730:
465:
2965:{\displaystyle P=P_{0}\cdot \left^{\textstyle {\frac {Mg}{R^{*}L}}}}
1590:{\displaystyle \rho =\rho _{b}{\frac {P}{T}}{\frac {T_{b}}{P_{b}}}}
1356:; the second equation is applicable to the standard model of the
263:{\displaystyle P=P_{b}\left^{\frac {g_{0}'M_{0}}{R^{*}L_{M,b}}}}
1360:
in which the temperature is assumed not to vary with altitude.
1325:
in which the temperature is assumed to vary with altitude at a
3086:
1794:= standard temperature lapse rate (see table below) (K/m) in
2127:= 1.2250 kg/m or 0.0023768908 slug/ft. Values of
27:
Formula used to model how air pressure varies with altitude
2728:{\displaystyle {\frac {dP}{P}}=-{\frac {Mg\,dz}{R^{*}T}}}
68:
Pressure as a function of the height above the sea level
2931:
2827:{\displaystyle P=P_{0}e^{-\int _{0}^{z}{Mgdz/R^{*}T}}}
2980:
2884:
2842:
2750:
2669:
2649:
2607:
2553:
2237:
2085:
2054:
2023:
1999:
1975:
1944:
1916:
1889:
1860:
1827:
1805:
1780:
1751:
1727:
1605:
1536:
1369:
1335:
921:
888:
841:
801:
779:
741:
702:
673:
642:
609:
576:
536:
514:
476:
437:
408:
280:
110:
83:
2046:= universal gas constant: 8.9494596×10 ft/(s·K)
935:= molar mass of Earth's air: 28.9644 lb/lb-mol
3036:
2964:
2870:
2826:
2727:
2655:
2635:
2587:
2243:
2101:= molar mass of Earth's air: 0.0289644 kg/mol
2093:
2069:
2038:
2007:
1983:
1959:
1924:
1903:= molar mass of Earth's air: 0.0289644 kg/mol
1895:
1873:
1840:
1811:
1786:
1764:
1735:
1708:
1589:
1518:
1348:
927:
901:
854:
814:
785:
760:
721:
686:
656:= molar mass of Earth's air: 0.0289644 kg/mol
648:
622:
589:
549:
520:
495:
456:
421:
391:
262:
96:
2740:this expression from the surface to the altitude
2543:The barometric formula can be derived using the
2077:= gravitational acceleration: 32.17405 ft/s
1881:= gravitational acceleration: 9.80665 m/s
1819:= height above sea level (geopotential meters)
793:= height at which pressure is calculated (ft)
8:
3125:
3123:
3066:(approximately equal to 8.4 km for the
2588:{\displaystyle P={\frac {\rho }{M}}{R^{*}}T}
2015:= height above sea level (geopotential feet)
528:= height at which pressure is calculated (m)
3145:
3143:
3141:
3139:
3023:
3014:
3001:
2991:
2979:
2947:
2932:
2930:
2918:
2909:
2895:
2883:
2853:
2841:
2812:
2803:
2790:
2784:
2779:
2771:
2761:
2749:
2713:
2700:
2691:
2670:
2668:
2648:
2626:
2606:
2575:
2570:
2560:
2552:
2236:
2086:
2084:
2060:
2055:
2053:
2029:
2024:
2022:
2000:
1998:
1976:
1974:
1950:
1945:
1943:
1917:
1915:
1888:
1865:
1859:
1832:
1826:
1804:
1779:
1756:
1750:
1728:
1726:
1709:{\displaystyle \rho =\rho _{b}\exp \left}
1693:
1683:
1666:
1642:
1632:
1616:
1604:
1579:
1569:
1563:
1553:
1547:
1535:
1494:
1484:
1469:
1462:
1456:
1444:
1433:
1420:
1398:
1391:
1380:
1368:
1340:
1334:
920:
893:
887:
846:
840:
806:
800:
778:
746:
740:
707:
701:
678:
672:
641:
614:
608:
581:
575:
541:
535:
513:
481:
475:
442:
436:
413:
407:
369:
364:
358:
341:
317:
307:
291:
279:
244:
234:
222:
209:
202:
188:
161:
145:
139:
121:
109:
88:
82:
2215:
2174:are each single-valued constants, while
1991:= standard temperature lapse rate (K/ft)
1049:
958:are each single-valued constants, while
63:
3119:
3037:{\displaystyle P=P_{0}e^{-Mgz/R^{*}T}}
7:
2120:= 0 is the defined sea level value,
1007:= 0 is the defined sea level value,
2836:Assuming linear temperature change
768:= temperature lapse rate (K/ft) in
503:= temperature lapse rate (K/m) in
25:
392:{\displaystyle P=P_{b}\exp \left}
866:; using feet, kelvins, and (SI)
2209:, 1976, and that the value for
2643:and dividing this equation by
2636:{\displaystyle dP=-\rho g\,dz}
2597:Assuming that all pressure is
1426:
1407:
194:
175:
1:
1018:or 29.92126 inHg. Values of
3089:for further understanding.)
2531:
2528:
2525:
2513:
2510:
2507:
2504:
2501:
2496:
2493:
2490:
2478:
2475:
2472:
2469:
2466:
2461:
2458:
2455:
2443:
2440:
2437:
2434:
2431:
2426:
2423:
2420:
2408:
2405:
2402:
2399:
2396:
2391:
2388:
2385:
2373:
2370:
2367:
2364:
2361:
2356:
2353:
2350:
2338:
2335:
2332:
2329:
2326:
2321:
2318:
2315:
2303:
2300:
2297:
2294:
2291:
822:= height of reference level
557:= height of reference level
3109:Vertical pressure variation
2205:are in accordance with the
988:are in accordance with the
3189:
2871:{\displaystyle T=T_{0}-Lz}
1967:= standard temperature (K)
1852:8.3144598 N·m/(mol·K)
1772:= standard temperature (K)
1311:
992:, 1976, and the value for
911:gravitational acceleration
879:10 lb·ft/(lb-mol·K·s)
632:gravitational acceleration
601:: 8.3144598 J/(mol·K)
57:
46:) of the air changes with
2262:
2253:
2230:
2224:
2218:
1075:
1072:
1067:
1064:
1058:
1052:
729:= reference temperature (
464:= reference temperature (
3150:U.S. Standard Atmosphere
2263:Temperature Lapse Rate (
2207:U.S. Standard Atmosphere
990:U.S. Standard Atmosphere
2105:The value of subscript
2070:{\displaystyle {g_{0}}}
2039:{\displaystyle {R^{*}}}
1960:{\displaystyle {T_{b}}}
1925:{\displaystyle {\rho }}
1736:{\displaystyle {\rho }}
1073:Temperature lapse rate
939:The value of subscript
761:{\displaystyle L_{M,b}}
722:{\displaystyle T_{M,b}}
496:{\displaystyle L_{M,b}}
457:{\displaystyle T_{M,b}}
3129:Mechtly, E. A., 1973:
3038:
2966:
2872:
2828:
2729:
2657:
2637:
2589:
2254:Standard Temperature (
2245:
2095:
2071:
2040:
2009:
1985:
1961:
1926:
1897:
1875:
1850:universal gas constant
1842:
1813:
1788:
1766:
1737:
1710:
1591:
1520:
1350:
929:
903:
864:universal gas constant
856:
816:
787:
762:
723:
688:
650:
624:
599:universal gas constant
591:
551:
522:
497:
458:
423:
393:
264:
98:
69:
38:used to model how the
3046:In this formulation,
3039:
2967:
2873:
2829:
2730:
2658:
2638:
2590:
2246:
2244:{\displaystyle \rho }
2227:height above MSL (h)
2096:
2072:
2041:
2010:
1986:
1962:
1927:
1898:
1876:
1874:{\displaystyle g_{0}}
1843:
1841:{\displaystyle R^{*}}
1814:
1789:
1767:
1765:{\displaystyle T_{b}}
1743:= mass density (kg/m)
1738:
1711:
1592:
1521:
1351:
1349:{\displaystyle L_{b}}
1312:Further information:
1061:height above MSL (h)
930:
904:
902:{\displaystyle g_{0}}
857:
855:{\displaystyle R^{*}}
817:
815:{\displaystyle h_{b}}
788:
763:
724:
689:
687:{\displaystyle P_{b}}
651:
625:
623:{\displaystyle g_{0}}
592:
590:{\displaystyle R^{*}}
552:
550:{\displaystyle h_{b}}
523:
498:
459:
424:
422:{\displaystyle P_{b}}
394:
265:
99:
97:{\displaystyle L_{b}}
67:
18:Isothermal atmosphere
3173:Atmospheric pressure
3099:Hypsometric equation
2978:
2882:
2840:
2748:
2667:
2647:
2605:
2551:
2235:
2159:In these equations,
2083:
2052:
2021:
1997:
1973:
1942:
1914:
1887:
1858:
1825:
1803:
1778:
1749:
1725:
1603:
1534:
1367:
1333:
1068:Standard temperature
919:
913:: 32.17405 ft/s
886:
839:
799:
777:
739:
700:
694:= reference pressure
671:
640:
607:
574:
534:
512:
474:
435:
429:= reference pressure
406:
278:
108:
81:
60:Atmospheric pressure
2789:
2094:{\displaystyle {M}}
2008:{\displaystyle {h}}
1984:{\displaystyle {L}}
1314:Atmospheric density
217:
3034:
2962:
2959:
2868:
2824:
2775:
2725:
2653:
2633:
2585:
2241:
2091:
2067:
2036:
2005:
1981:
1957:
1922:
1893:
1871:
1838:
1809:
1784:
1762:
1733:
1706:
1587:
1516:
1346:
925:
899:
852:
812:
783:
758:
719:
684:
646:
634:: 9.80665 m/s
620:
587:
547:
518:
493:
454:
419:
389:
260:
205:
94:
70:
54:Pressure equations
32:barometric formula
3168:Vertical position
2957:
2924:
2723:
2683:
2656:{\displaystyle P}
2568:
2536:
2535:
1896:{\displaystyle M}
1812:{\displaystyle h}
1787:{\displaystyle L}
1700:
1585:
1561:
1501:
1450:
1308:Density equations
1305:
1304:
928:{\displaystyle M}
833:= 36,089 ft)
786:{\displaystyle h}
649:{\displaystyle M}
521:{\displaystyle h}
383:
257:
173:
16:(Redirected from
3180:
3153:
3147:
3134:
3127:
3043:
3041:
3040:
3035:
3033:
3032:
3028:
3027:
3018:
2996:
2995:
2971:
2969:
2968:
2963:
2961:
2960:
2958:
2956:
2952:
2951:
2941:
2933:
2929:
2925:
2923:
2922:
2910:
2900:
2899:
2877:
2875:
2874:
2869:
2858:
2857:
2833:
2831:
2830:
2825:
2823:
2822:
2821:
2817:
2816:
2807:
2788:
2783:
2766:
2765:
2734:
2732:
2731:
2726:
2724:
2722:
2718:
2717:
2707:
2692:
2684:
2679:
2671:
2662:
2660:
2659:
2654:
2642:
2640:
2639:
2634:
2594:
2592:
2591:
2586:
2581:
2580:
2579:
2569:
2561:
2523:
2521:
2518:
2488:
2486:
2483:
2453:
2451:
2448:
2418:
2416:
2413:
2383:
2381:
2378:
2348:
2346:
2343:
2313:
2311:
2308:
2250:
2248:
2247:
2242:
2216:
2100:
2098:
2097:
2092:
2090:
2076:
2074:
2073:
2068:
2066:
2065:
2064:
2045:
2043:
2042:
2037:
2035:
2034:
2033:
2014:
2012:
2011:
2006:
2004:
1990:
1988:
1987:
1982:
1980:
1966:
1964:
1963:
1958:
1956:
1955:
1954:
1932:= mass density (
1931:
1929:
1928:
1923:
1921:
1902:
1900:
1899:
1894:
1880:
1878:
1877:
1872:
1870:
1869:
1847:
1845:
1844:
1839:
1837:
1836:
1818:
1816:
1815:
1810:
1793:
1791:
1790:
1785:
1771:
1769:
1768:
1763:
1761:
1760:
1742:
1740:
1739:
1734:
1732:
1715:
1713:
1712:
1707:
1705:
1701:
1699:
1698:
1697:
1688:
1687:
1677:
1676:
1672:
1671:
1670:
1647:
1646:
1633:
1621:
1620:
1596:
1594:
1593:
1588:
1586:
1584:
1583:
1574:
1573:
1564:
1562:
1554:
1552:
1551:
1525:
1523:
1522:
1517:
1515:
1514:
1513:
1509:
1502:
1500:
1499:
1498:
1489:
1488:
1478:
1474:
1473:
1463:
1455:
1451:
1449:
1448:
1439:
1438:
1437:
1425:
1424:
1403:
1402:
1392:
1385:
1384:
1355:
1353:
1352:
1347:
1345:
1344:
1065:Static pressure
1050:
934:
932:
931:
926:
908:
906:
905:
900:
898:
897:
880:
878:
875:
861:
859:
858:
853:
851:
850:
821:
819:
818:
813:
811:
810:
792:
790:
789:
784:
767:
765:
764:
759:
757:
756:
728:
726:
725:
720:
718:
717:
693:
691:
690:
685:
683:
682:
660:Or converted to
655:
653:
652:
647:
629:
627:
626:
621:
619:
618:
596:
594:
593:
588:
586:
585:
568:= 11 000 m)
556:
554:
553:
548:
546:
545:
527:
525:
524:
519:
502:
500:
499:
494:
492:
491:
463:
461:
460:
455:
453:
452:
428:
426:
425:
420:
418:
417:
398:
396:
395:
390:
388:
384:
382:
381:
380:
379:
363:
362:
352:
351:
347:
346:
345:
322:
321:
308:
296:
295:
269:
267:
266:
261:
259:
258:
256:
255:
254:
239:
238:
228:
227:
226:
213:
203:
201:
197:
193:
192:
174:
172:
171:
156:
155:
140:
126:
125:
103:
101:
100:
95:
93:
92:
21:
3188:
3187:
3183:
3182:
3181:
3179:
3178:
3177:
3158:
3157:
3156:
3148:
3137:
3128:
3121:
3117:
3095:
3054:, and the term
3019:
2997:
2987:
2976:
2975:
2943:
2942:
2934:
2914:
2905:
2904:
2891:
2880:
2879:
2849:
2838:
2837:
2808:
2767:
2757:
2746:
2745:
2709:
2708:
2693:
2672:
2665:
2664:
2645:
2644:
2603:
2602:
2571:
2549:
2548:
2541:
2519:
2516:
2514:
2484:
2481:
2479:
2449:
2446:
2444:
2414:
2411:
2409:
2379:
2376:
2374:
2344:
2341:
2339:
2309:
2306:
2304:
2259:
2233:
2232:
2200:
2165:
2155:
2132:
2126:
2114:
2081:
2080:
2056:
2050:
2049:
2025:
2019:
2018:
1995:
1994:
1971:
1970:
1946:
1940:
1939:
1912:
1911:
1885:
1884:
1861:
1856:
1855:
1828:
1823:
1822:
1801:
1800:
1776:
1775:
1752:
1747:
1746:
1723:
1722:
1689:
1679:
1678:
1662:
1655:
1651:
1638:
1634:
1628:
1612:
1601:
1600:
1575:
1565:
1543:
1532:
1531:
1490:
1480:
1479:
1465:
1464:
1461:
1457:
1440:
1429:
1416:
1394:
1393:
1387:
1386:
1376:
1365:
1364:
1336:
1331:
1330:
1316:
1310:
1077:
1069:
1046:
1023:
1013:
1001:
983:
949:
917:
916:
889:
884:
883:
876:
873:
871:
842:
837:
836:
831:
802:
797:
796:
775:
774:
742:
737:
736:
703:
698:
697:
674:
669:
668:
638:
637:
610:
605:
604:
577:
572:
571:
566:
561:(meters; e.g.,
537:
532:
531:
510:
509:
477:
472:
471:
438:
433:
432:
409:
404:
403:
365:
354:
353:
337:
330:
326:
313:
309:
303:
287:
276:
275:
240:
230:
229:
218:
204:
184:
157:
141:
132:
128:
127:
117:
106:
105:
84:
79:
78:
62:
56:
28:
23:
22:
15:
12:
11:
5:
3186:
3184:
3176:
3175:
3170:
3160:
3159:
3155:
3154:
3135:
3118:
3116:
3113:
3112:
3111:
3106:
3101:
3094:
3091:
3031:
3026:
3022:
3017:
3013:
3010:
3007:
3004:
3000:
2994:
2990:
2986:
2983:
2955:
2950:
2946:
2940:
2937:
2928:
2921:
2917:
2913:
2908:
2903:
2898:
2894:
2890:
2887:
2867:
2864:
2861:
2856:
2852:
2848:
2845:
2820:
2815:
2811:
2806:
2802:
2799:
2796:
2793:
2787:
2782:
2778:
2774:
2770:
2764:
2760:
2756:
2753:
2721:
2716:
2712:
2706:
2703:
2699:
2696:
2690:
2687:
2682:
2678:
2675:
2652:
2632:
2629:
2625:
2622:
2619:
2616:
2613:
2610:
2584:
2578:
2574:
2567:
2564:
2559:
2556:
2540:
2537:
2534:
2533:
2530:
2527:
2524:
2512:
2509:
2506:
2503:
2499:
2498:
2495:
2492:
2489:
2477:
2474:
2471:
2468:
2464:
2463:
2460:
2457:
2454:
2442:
2439:
2436:
2433:
2429:
2428:
2425:
2422:
2419:
2407:
2404:
2401:
2398:
2394:
2393:
2390:
2387:
2384:
2372:
2369:
2366:
2363:
2359:
2358:
2355:
2352:
2349:
2337:
2334:
2331:
2328:
2324:
2323:
2320:
2317:
2314:
2302:
2299:
2296:
2293:
2289:
2288:
2285:
2282:
2279:
2276:
2273:
2269:
2268:
2261:
2252:
2240:
2231:Mass Density (
2229:
2223:
2198:
2163:
2150:
2130:
2124:
2112:
2103:
2102:
2089:
2078:
2063:
2059:
2047:
2032:
2028:
2016:
2003:
1992:
1979:
1968:
1953:
1949:
1937:
1920:
1905:
1904:
1892:
1882:
1868:
1864:
1853:
1835:
1831:
1820:
1808:
1798:
1783:
1773:
1759:
1755:
1744:
1731:
1704:
1696:
1692:
1686:
1682:
1675:
1669:
1665:
1661:
1658:
1654:
1650:
1645:
1641:
1637:
1631:
1627:
1624:
1619:
1615:
1611:
1608:
1582:
1578:
1572:
1568:
1560:
1557:
1550:
1546:
1542:
1539:
1512:
1508:
1505:
1497:
1493:
1487:
1483:
1477:
1472:
1468:
1460:
1454:
1447:
1443:
1436:
1432:
1428:
1423:
1419:
1415:
1412:
1409:
1406:
1401:
1397:
1390:
1383:
1379:
1375:
1372:
1343:
1339:
1309:
1306:
1303:
1302:
1299:
1296:
1293:
1290:
1287:
1284:
1281:
1278:
1274:
1273:
1270:
1267:
1264:
1261:
1258:
1255:
1252:
1249:
1245:
1244:
1241:
1238:
1235:
1232:
1229:
1226:
1223:
1220:
1216:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1187:
1186:
1183:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1158:
1157:
1154:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1129:
1128:
1125:
1122:
1119:
1116:
1113:
1110:
1107:
1104:
1100:
1099:
1096:
1093:
1090:
1087:
1084:
1080:
1079:
1074:
1071:
1066:
1063:
1057:
1041:
1021:
1011:
999:
981:
947:
937:
936:
924:
914:
896:
892:
881:
849:
845:
834:
829:
809:
805:
794:
782:
772:
755:
752:
749:
745:
734:
716:
713:
710:
706:
695:
681:
677:
662:imperial units
658:
657:
645:
635:
617:
613:
602:
584:
580:
569:
564:
544:
540:
529:
517:
507:
490:
487:
484:
480:
469:
451:
448:
445:
441:
430:
416:
412:
387:
378:
375:
372:
368:
361:
357:
350:
344:
340:
336:
333:
329:
325:
320:
316:
312:
306:
302:
299:
294:
290:
286:
283:
253:
250:
247:
243:
237:
233:
225:
221:
216:
212:
208:
200:
196:
191:
187:
183:
180:
177:
170:
167:
164:
160:
154:
151:
148:
144:
138:
135:
131:
124:
120:
116:
113:
91:
87:
55:
52:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3185:
3174:
3171:
3169:
3166:
3165:
3163:
3151:
3146:
3144:
3142:
3140:
3136:
3132:
3126:
3124:
3120:
3114:
3110:
3107:
3105:
3102:
3100:
3097:
3096:
3092:
3090:
3088:
3084:
3080:
3076:
3071:
3069:
3065:
3061:
3057:
3053:
3049:
3044:
3029:
3024:
3020:
3015:
3011:
3008:
3005:
3002:
2998:
2992:
2988:
2984:
2981:
2972:
2953:
2948:
2944:
2938:
2935:
2926:
2919:
2915:
2911:
2906:
2901:
2896:
2892:
2888:
2885:
2865:
2862:
2859:
2854:
2850:
2846:
2843:
2834:
2818:
2813:
2809:
2804:
2800:
2797:
2794:
2791:
2785:
2780:
2776:
2772:
2768:
2762:
2758:
2754:
2751:
2743:
2739:
2735:
2719:
2714:
2710:
2704:
2701:
2697:
2694:
2688:
2685:
2680:
2676:
2673:
2650:
2630:
2627:
2623:
2620:
2617:
2614:
2611:
2608:
2600:
2595:
2582:
2576:
2572:
2565:
2562:
2557:
2554:
2546:
2545:ideal gas law
2538:
2500:
2465:
2430:
2395:
2360:
2325:
2290:
2286:
2283:
2280:
2277:
2274:
2271:
2270:
2266:
2257:
2238:
2228:
2225:Geopotential
2222:
2217:
2214:
2212:
2208:
2204:
2197:
2193:
2189:
2185:
2181:
2177:
2173:
2169:
2162:
2157:
2153:
2149:
2145:
2141:
2137:
2133:
2123:
2119:
2115:
2108:
2087:
2079:
2061:
2057:
2048:
2030:
2026:
2017:
2001:
1993:
1977:
1969:
1951:
1947:
1938:
1935:
1918:
1910:
1909:
1908:
1890:
1883:
1866:
1862:
1854:
1851:
1833:
1829:
1821:
1806:
1799:
1797:
1781:
1774:
1757:
1753:
1745:
1729:
1721:
1720:
1719:
1716:
1702:
1694:
1690:
1684:
1680:
1673:
1667:
1663:
1659:
1656:
1652:
1648:
1643:
1639:
1635:
1629:
1625:
1622:
1617:
1613:
1609:
1606:
1597:
1580:
1576:
1570:
1566:
1558:
1555:
1548:
1544:
1540:
1537:
1529:
1526:
1510:
1506:
1503:
1495:
1491:
1485:
1481:
1475:
1470:
1466:
1458:
1452:
1445:
1441:
1434:
1430:
1421:
1417:
1413:
1410:
1404:
1399:
1395:
1388:
1381:
1377:
1373:
1370:
1361:
1359:
1341:
1337:
1328:
1324:
1319:
1315:
1307:
1300:
1297:
1294:
1291:
1288:
1285:
1282:
1279:
1276:
1275:
1271:
1268:
1265:
1262:
1259:
1256:
1253:
1250:
1247:
1246:
1242:
1239:
1236:
1233:
1230:
1227:
1224:
1221:
1218:
1217:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1188:
1184:
1181:
1178:
1175:
1172:
1169:
1166:
1163:
1160:
1159:
1155:
1152:
1149:
1146:
1143:
1140:
1137:
1134:
1131:
1130:
1126:
1123:
1120:
1117:
1114:
1111:
1108:
1105:
1102:
1101:
1097:
1094:
1091:
1088:
1085:
1082:
1081:
1062:
1059:Geopotential
1056:
1051:
1048:
1044:
1040:
1036:
1032:
1028:
1024:
1017:
1010:
1006:
1002:
995:
991:
987:
980:
976:
972:
968:
965:
961:
957:
953:
946:
942:
922:
915:
912:
894:
890:
882:
869:
865:
847:
843:
835:
832:
826:(feet; e.g.,
825:
807:
803:
795:
780:
773:
771:
753:
750:
747:
743:
735:
732:
714:
711:
708:
704:
696:
679:
675:
667:
666:
665:
663:
643:
636:
633:
615:
611:
603:
600:
582:
578:
570:
567:
560:
542:
538:
530:
515:
508:
506:
488:
485:
482:
478:
470:
467:
449:
446:
443:
439:
431:
414:
410:
402:
401:
400:
385:
376:
373:
370:
366:
359:
355:
348:
342:
338:
334:
331:
327:
323:
318:
314:
310:
304:
300:
297:
292:
288:
284:
281:
273:
251:
248:
245:
241:
235:
231:
223:
219:
214:
210:
206:
198:
189:
185:
181:
178:
168:
165:
162:
158:
152:
149:
146:
142:
136:
133:
129:
122:
118:
114:
111:
89:
85:
76:
66:
61:
53:
51:
49:
45:
41:
37:
33:
19:
3130:
3074:
3072:
3064:scale height
3059:
3055:
3052:gas constant
3047:
3045:
2973:
2835:
2741:
2736:
2596:
2542:
2505:71 000
2470:51 000
2435:47 000
2427:-0.00085344
2400:32 000
2365:20 000
2330:11 000
2264:
2255:
2226:
2220:
2210:
2202:
2195:
2191:
2187:
2183:
2179:
2175:
2171:
2167:
2160:
2158:
2151:
2147:
2143:
2139:
2138:= 1 through
2135:
2128:
2121:
2117:
2110:
2106:
2104:
1906:
1717:
1599:Equation 2:
1598:
1530:
1527:
1363:Equation 1:
1362:
1358:stratosphere
1320:
1317:
1060:
1054:
1042:
1038:
1034:
1030:
1029:= 1 through
1026:
1019:
1008:
1004:
997:
993:
985:
978:
974:
970:
966:
963:
959:
955:
951:
944:
940:
938:
827:
823:
659:
562:
558:
71:
31:
29:
3104:NRLMSISE-00
3083:perfect gas
3068:troposphere
2738:Integrating
2599:hydrostatic
2508:232,939.63
2497:0.00085344
2473:167,322.83
2438:154,199.48
2403:104,986.87
2392:-0.0003048
1323:troposphere
1280:71 000
1251:51 000
1222:47 000
1211:-0.00085344
1193:32 000
1164:20 000
1135:11 000
1078:g0 M / R L
3162:Categories
3115:References
3062:gives the
2539:Derivation
2532:0.0006096
2368:65,616.79
2333:36,089.24
2322:0.0019812
2219:Subscript
1327:lapse rate
1289:0.00116833
1269:0.00085344
1260:0.01976704
1182:-0.0003048
1112:101 325.00
1053:Subscript
1014:= 101 325
274:is null):
272:lapse rate
75:lapse rate
58:See also:
3075:ideal gas
3025:∗
3003:−
2949:∗
2902:⋅
2860:−
2814:∗
2777:∫
2773:−
2715:∗
2689:−
2621:ρ
2618:−
2577:∗
2563:ρ
2511:0.000064
2281:(slug/ft)
2239:ρ
2031:∗
1919:ρ
1834:∗
1730:ρ
1685:∗
1660:−
1636:−
1626:
1614:ρ
1607:ρ
1545:ρ
1538:ρ
1504:−
1486:∗
1414:−
1405:−
1378:ρ
1371:ρ
1298:0.0006096
1231:0.0327506
1214:-12.2009
1202:0.2563258
1185:-34.1626
1141:22 632.10
1124:0.0019812
1076:Exponent
848:∗
583:∗
360:∗
335:−
311:−
301:
236:∗
182:−
137:−
3093:See also
3079:real gas
2744:we get:
2663:we get:
2476:0.00086
2441:0.00143
2424:-0.0028
2406:0.01322
2371:0.08803
2336:0.36391
1301:17.0813
1272:12.2009
1243:—
1173:1.616734
1156:—
1144:6.683245
1127:5.25588
1115:29.92126
215:′
48:altitude
40:pressure
3050:is the
2526:214.65
2494:0.0028
2491:270.65
2456:270.65
2421:228.65
2389:-0.001
2386:216.65
2351:216.65
2319:0.0065
2316:288.15
2301:1.2250
2287:(K/ft)
1283:232,940
1254:167,323
1225:154,199
1208:-0.0028
1196:104,987
1170:5474.89
1098:(K/ft)
399:where:
44:density
36:formula
3077:. See
2529:0.002
2278:(kg/m)
1718:where
1292:214.65
1266:0.0028
1263:270.65
1234:270.65
1228:110.91
1205:228.65
1199:868.02
1179:-0.001
1176:216.65
1167:65,617
1147:216.65
1138:36,089
1121:0.0065
1118:288.15
1092:(inHg)
984:, and
2515:1.245
2480:1.671
2445:2.769
2410:2.566
2375:1.708
2340:7.061
2305:2.376
2284:(K/m)
1295:0.002
1257:66.94
1095:(K/m)
872:8.949
868:moles
34:is a
2517:8989
2482:7895
2462:0.0
2459:0.0
2447:8702
2412:0735
2377:1572
2357:0.0
2354:0.0
2342:1703
2307:8908
2275:(ft)
2260:(K)
2201:and
2186:and
2170:and
2116:for
1936:/ft)
1934:slug
1286:3.96
1089:(Pa)
1086:(ft)
1070:(K)
1003:for
969:and
954:and
874:4596
42:(or
30:The
3087:gas
3085:or
3081:or
3070:).
2272:(m)
2134:of
1796:ISA
1623:exp
1329:of
1240:0.0
1237:0.0
1153:0.0
1150:0.0
1083:(m)
1025:of
770:ISA
505:ISA
298:exp
77:of
3164::
3138:^
3122:^
3060:Mg
3056:RT
2601::
2547::
2522:10
2502:6
2487:10
2467:5
2452:10
2432:4
2417:10
2397:3
2382:10
2362:2
2347:10
2327:1
2312:10
2298:0
2295:0
2292:0
2267:)
2256:T'
2251:)
2194:,
2182:,
2178:,
2166:,
2156:.
2154:+1
2146:=
1848:=
1047:.
1045:+1
1037:=
1016:Pa
977:,
967:T,
964:L,
962:,
950:,
909:=
870::
862:=
664::
630:=
597:=
104::
50:.
3058:/
3048:R
3030:T
3021:R
3016:/
3012:z
3009:g
3006:M
2999:e
2993:0
2989:P
2985:=
2982:P
2954:L
2945:R
2939:g
2936:M
2927:]
2920:0
2916:T
2912:T
2907:[
2897:0
2893:P
2889:=
2886:P
2866:z
2863:L
2855:0
2851:T
2847:=
2844:T
2819:T
2810:R
2805:/
2801:z
2798:d
2795:g
2792:M
2786:z
2781:0
2769:e
2763:0
2759:P
2755:=
2752:P
2742:z
2720:T
2711:R
2705:z
2702:d
2698:g
2695:M
2686:=
2681:P
2677:P
2674:d
2651:P
2631:z
2628:d
2624:g
2615:=
2612:P
2609:d
2583:T
2573:R
2566:M
2558:=
2555:P
2520:×
2485:×
2450:×
2415:×
2380:×
2345:×
2310:×
2265:L
2258:)
2221:b
2211:R
2203:R
2199:0
2196:g
2192:M
2188:h
2184:T
2180:L
2176:ρ
2172:R
2168:M
2164:0
2161:g
2152:b
2148:h
2144:h
2140:b
2136:b
2131:b
2129:ρ
2125:0
2122:ρ
2118:b
2113:b
2111:ρ
2107:b
2088:M
2062:0
2058:g
2027:R
2002:h
1978:L
1952:b
1948:T
1891:M
1867:0
1863:g
1830:R
1807:h
1782:L
1758:b
1754:T
1703:]
1695:b
1691:T
1681:R
1674:)
1668:b
1664:h
1657:h
1653:(
1649:M
1644:0
1640:g
1630:[
1618:b
1610:=
1581:b
1577:P
1571:b
1567:T
1559:T
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1549:b
1541:=
1511:)
1507:1
1496:b
1492:L
1482:R
1476:M
1471:0
1467:g
1459:(
1453:]
1446:b
1442:T
1435:b
1431:L
1427:)
1422:b
1418:h
1411:h
1408:(
1400:b
1396:T
1389:[
1382:b
1374:=
1342:b
1338:L
1277:6
1248:5
1219:4
1190:3
1161:2
1132:1
1109:0
1106:0
1103:0
1055:b
1043:b
1039:h
1035:h
1031:b
1027:b
1022:b
1020:P
1012:0
1009:P
1005:b
1000:b
998:P
994:R
986:R
982:0
979:g
975:M
971:h
960:P
956:R
952:M
948:0
945:g
941:b
923:M
895:0
891:g
877:×
844:R
830:b
828:h
824:b
808:b
804:h
781:h
754:b
751:,
748:M
744:L
733:)
731:K
715:b
712:,
709:M
705:T
680:b
676:P
644:M
616:0
612:g
579:R
565:b
563:h
559:b
543:b
539:h
516:h
489:b
486:,
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479:L
468:)
466:K
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447:,
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440:T
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386:]
377:b
374:,
371:M
367:T
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349:)
343:b
339:h
332:h
328:(
324:M
319:0
315:g
305:[
293:b
289:P
285:=
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252:b
249:,
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224:0
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199:]
195:)
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186:h
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176:(
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150:,
147:M
143:L
134:1
130:[
123:b
119:P
115:=
112:P
90:b
86:L
20:)
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