. "A lei de Laplace (em honra ao f\u00EDsico e matem\u00E1tico franc\u00EAs Pierre Simon Laplace) as vezes chamada lei de Laplace-Young ou equa\u00E7\u00E3o de Young\u2013Laplace (por Thomas Young) \u00E9 uma lei da f\u00EDsica que relaciona a varia\u00E7\u00E3o de press\u00E3o na superf\u00EDcie que separa dois fluidos de distinta natureza com as for\u00E7as de liga\u00E7\u00E3o molecular. Em sua forma mais geral pode ser expressada como: Onde \u0394P \u00E9 a varia\u00E7\u00E3o de press\u00E3o entre superf\u00EDcies (sempre maior no lado c\u00F4ncavo), =Tens\u00E3o superficial e ambas R sao dois raios de curvaturas perpendiculares. As vezes se usa H = , sendo H a curvatura da superf\u00EDcie. Desse modo, percebe-se que a varia\u00E7\u00E3o de press\u00F5es em um ponto da superf\u00EDcie s\u00F3 depende do valor da tens\u00E3o superficial e da curvatura m\u00E9dia da superf\u00EDcie nesse ponto."@pt . . . . . . . . . . "La ley de Laplace es una ley f\u00EDsica que relaciona el cambio de presiones en la superficie que separa dos fluidos de distinta naturaleza con las fuerzas de l\u00EDnea debidas a efectos moleculares."@es . . . . . . . . "\u0417\u0430\u043A\u043E\u043D \u041B\u0430\u043F\u043B\u0430\u0441\u0430"@uk . "\u30E4\u30F3\u30B0\u30FB\u30E9\u30D7\u30E9\u30B9\u306E\u5F0F"@ja . "A pendant drop is produced for an over pressure of \u0394p*=3 and initial condition r0=10\u22124, z0=0, dz/dr=0"@en . "YoungLaplace example drop.gif"@en . . . "9122581"^^ . "Relazione di Laplace"@it . . . . . . "YoungLaplace example bridge.gif"@en . . . "vertical"@en . . . "Die Young-Laplace-Gleichung (nach Thomas Young und Pierre-Simon Laplace, die sie unabh\u00E4ngig voneinander 1805 herleiteten) beschreibt den Zusammenhang zwischen der Oberfl\u00E4chenspannung, dem Druck und der Oberfl\u00E4chenkr\u00FCmmung einer Fl\u00FCssigkeit. In der Physiologie ist sie als Laplace-Gesetz bekannt und wird dort allgemeiner zur Beschreibung von Dr\u00FCcken in Hohlorganen verwendet, unabh\u00E4ngig davon, ob die Kraft an der Grenzfl\u00E4che von einer Oberfl\u00E4chenspannung herr\u00FChrt."@de . . . . . . . . . "La pression de Laplace, ou pression capillaire, est la diff\u00E9rence de pression entre les deux c\u00F4t\u00E9s d'une interface courbe s\u00E9parant deux milieux fluides. Par extension, elle d\u00E9signe aussi la diff\u00E9rence de pression \u00E0 travers une interface (courbe ou plane) s\u00E9parant un milieu solide d'un milieu fluide."@fr . . . "\u0417\u0430\u043A\u043E\u043D \u041B\u0430\u043F\u043B\u0430\u0441\u0430 \u2014 \u043F\u0440\u044F\u043C\u043E \u043F\u0440\u043E\u043F\u043E\u0440\u0446\u0456\u0439\u043D\u0430 \u0437\u0430\u043B\u0435\u0436\u043D\u0456\u0441\u0442\u044C \u043A\u0430\u043F\u0456\u043B\u044F\u0440\u043D\u043E\u0433\u043E \u0442\u0438\u0441\u043A\u0443 \u0432\u0456\u0434 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0435\u0432\u043E\u0433\u043E \u043D\u0430\u0442\u044F\u0433\u0443 \u043D\u0430 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456 \u0440\u043E\u0437\u0434\u0456\u043B\u0443 \u0434\u0432\u043E\u0445 \u0440\u0456\u0434\u0438\u043D \u0430\u0431\u043E \u0440\u0456\u0434\u0438\u043D\u0438 \u0456 \u0433\u0430\u0437\u0443 \u0456 \u0432\u0456\u0434 \u0441\u0435\u0440\u0435\u0434\u043D\u044C\u043E\u0457 \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456 (\u0442\u043E\u0431\u0442\u043E .\u0422\u0443\u0442 \u0456 \u2014 \u0433\u043E\u043B\u043E\u0432\u043D\u0456 \u0440\u0430\u0434\u0456\u0443\u0441\u0438 \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u0434\u0432\u043E\u0445 \u0432\u0437\u0430\u0454\u043C\u043D\u043E \u043F\u0435\u0440\u043F\u0435\u043D\u0434\u0438\u043A\u0443\u043B\u044F\u0440\u043D\u0438\u0445 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0438\u0445 \u043F\u0435\u0440\u0435\u0440\u0456\u0437\u0456\u0432 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456): \u0426\u0435\u0439 \u0437\u0430\u043A\u043E\u043D \u0454 \u043E\u0434\u043D\u0438\u043C \u0437 \u043E\u0441\u043D\u043E\u0432\u043D\u0438\u0445 \u0437\u0430\u043A\u043E\u043D\u0456\u0432 \u043A\u0430\u043F\u0456\u043B\u044F\u0440\u043D\u0438\u0445 \u044F\u0432\u0438\u0449. \u0419\u043E\u0433\u043E \u0432\u0456\u0434\u043A\u0440\u0438\u0432 \u041F. \u0421. \u041B\u0430\u043F\u043B\u0430\u0441 \u0432 1806 \u0440\u043E\u0446\u0456."@uk . . . "La pression de Laplace, ou pression capillaire, est la diff\u00E9rence de pression entre les deux c\u00F4t\u00E9s d'une interface courbe s\u00E9parant deux milieux fluides. Par extension, elle d\u00E9signe aussi la diff\u00E9rence de pression \u00E0 travers une interface (courbe ou plane) s\u00E9parant un milieu solide d'un milieu fluide. La loi de Laplace, ou \u00E9quation de Laplace-Young, relie la pression de Laplace \u00E0 la courbure moyenne de l'interface et \u00E0 sa tension superficielle. Ainsi, la pression est plus grande dans une goutte de pluie ou dans une bulle de savon que dans l'atmosph\u00E8re qui l'entoure, et la diff\u00E9rence de pression est d'autant plus grande que la goutte ou la bulle est plus petite."@fr . . . . . . . . . . . . . "\u694A-\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u5F0F\u662F\u4E00\u975E\u7DDA\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u7528\u4F86\u8A08\u7B97\u5169\u975C\u614B\u6D41\u9AD4\u754C\u9593\u56E0\u8868\u9762\u5F35\u529B\u6216\u58C1\u5F35\u529B\u9020\u6210\u7684\u6BDB\u7D30\u7BA1\u58D3\u529B\u5DEE\uFF0C\u5982\u6C34\u8207\u7A7A\u6C23\u3002\u694A-\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u5F0F\u9023\u7D50\u4E86\u6B64\u58D3\u529B\u5DEE\u8207\u8868\u9762\u5F62\u8C8C\u7684\u95DC\u4FC2\uFF0C\u5C0D\u975C\u614B\u6BDB\u7D30\u7BA1\u8868\u9762\u7684\u7814\u7A76\u5F88\u6709\u5E6B\u52A9\u3002\u6B64\u65B9\u7A0B\u5F0F\u63CF\u8FF0\u4E86\u6DB2\u9AD4\u754C\u9762\u9593\u6B63\u5411\u58D3\u529B\u7684\u5E73\u8861(\u754C\u9762\u539A\u5EA6\u70BA\u96F6)\u3002 \uFF1A\u754C\u9762\u9593\u7684\u58D3\u529B\u5DEE\u3001\u03B3\uFF1A\u8868\u9762\u5F35\u529B\u4FC2\u6578\u3001\uFF1A\u5F80\u754C\u9762\u5916\u7684\u55AE\u4F4D\u6CD5\u5411\u91CF\u3001\uFF1A\u5E73\u5747\u66F2\u7387\u3001\u8207\uFF1A\u4E3B\u8981\u66F2\u7387\u534A\u5F91 \u5728\u6B64\u53EA\u8003\u616E\u6B63\u5411\u58D3\u529B\uFF0C\u56E0\u5207\u7DDA\u65B9\u5411\u58D3\u529B\u5B58\u5728\u6703\u5C0E\u81F4\u754C\u9762\u7684\u4E0D\u7A69\u5B9A\u3002"@zh . . . . "16750"^^ . . . . "Die Young-Laplace-Gleichung (nach Thomas Young und Pierre-Simon Laplace, die sie unabh\u00E4ngig voneinander 1805 herleiteten) beschreibt den Zusammenhang zwischen der Oberfl\u00E4chenspannung, dem Druck und der Oberfl\u00E4chenkr\u00FCmmung einer Fl\u00FCssigkeit. In der Physiologie ist sie als Laplace-Gesetz bekannt und wird dort allgemeiner zur Beschreibung von Dr\u00FCcken in Hohlorganen verwendet, unabh\u00E4ngig davon, ob die Kraft an der Grenzfl\u00E4che von einer Oberfl\u00E4chenspannung herr\u00FChrt."@de . . . . . . "Ley de Laplace"@es . . . . . . . "Young-Laplace-Gleichung"@de . . . . . . . "220"^^ . . . . . . . "Young\u2013Laplace equation"@en . "\u694A-\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u5F0F\u662F\u4E00\u975E\u7DDA\u6027\u504F\u5FAE\u5206\u65B9\u7A0B\uFF0C\u7528\u4F86\u8A08\u7B97\u5169\u975C\u614B\u6D41\u9AD4\u754C\u9593\u56E0\u8868\u9762\u5F35\u529B\u6216\u58C1\u5F35\u529B\u9020\u6210\u7684\u6BDB\u7D30\u7BA1\u58D3\u529B\u5DEE\uFF0C\u5982\u6C34\u8207\u7A7A\u6C23\u3002\u694A-\u62C9\u666E\u62C9\u65AF\u65B9\u7A0B\u5F0F\u9023\u7D50\u4E86\u6B64\u58D3\u529B\u5DEE\u8207\u8868\u9762\u5F62\u8C8C\u7684\u95DC\u4FC2\uFF0C\u5C0D\u975C\u614B\u6BDB\u7D30\u7BA1\u8868\u9762\u7684\u7814\u7A76\u5F88\u6709\u5E6B\u52A9\u3002\u6B64\u65B9\u7A0B\u5F0F\u63CF\u8FF0\u4E86\u6DB2\u9AD4\u754C\u9762\u9593\u6B63\u5411\u58D3\u529B\u7684\u5E73\u8861(\u754C\u9762\u539A\u5EA6\u70BA\u96F6)\u3002 \uFF1A\u754C\u9762\u9593\u7684\u58D3\u529B\u5DEE\u3001\u03B3\uFF1A\u8868\u9762\u5F35\u529B\u4FC2\u6578\u3001\uFF1A\u5F80\u754C\u9762\u5916\u7684\u55AE\u4F4D\u6CD5\u5411\u91CF\u3001\uFF1A\u5E73\u5747\u66F2\u7387\u3001\u8207\uFF1A\u4E3B\u8981\u66F2\u7387\u534A\u5F91 \u5728\u6B64\u53EA\u8003\u616E\u6B63\u5411\u58D3\u529B\uFF0C\u56E0\u5207\u7DDA\u65B9\u5411\u58D3\u529B\u5B58\u5728\u6703\u5C0E\u81F4\u754C\u9762\u7684\u4E0D\u7A69\u5B9A\u3002"@zh . "Lei de Laplace"@pt . . . "\u30E4\u30F3\u30B0\u30FB\u30E9\u30D7\u30E9\u30B9\u306E\u5F0F\u3068\u306F\u3001\u66F2\u7387\u3092\u3082\u3064\u6C17\u76F8\u30FB\u6DB2\u76F8\u306E\u754C\u9762\u306B\u304A\u3044\u3066\u30012\u76F8\u9593\u306E\u5727\u529B\u5DEE\u3068\u754C\u9762\u306E\u66F2\u7387\u3092\u95A2\u9023\u4ED8\u3051\u308B\u65B9\u7A0B\u5F0F\u3067\u3042\u308B\u3002\u8868\u9762\u5F35\u529B\u3092\u03B3\u3001\u754C\u9762\u306E2\u3064\u306E\u66F2\u7387\u534A\u5F84\u3092R1, R2\u3068\u3059\u308B\u3068\u3001\u5727\u529B\u5DEE\u0394p\uFF08\u30E9\u30D7\u30E9\u30B9\u5727\u3082\u3057\u304F\u306F\u6BDB\u7BA1\u5727\u3068\u547C\u3070\u308C\u308B\uFF09\u306F\u6B21\u5F0F\u3067\u8868\u3055\u308C\u308B\uFF1A \u8868\u9762\u5F35\u529B\u306F\u754C\u9762\u3092\u6700\u5C0F\u5316\u3059\u308B\u3088\u3046\u306B\u306F\u305F\u3089\u304F\u305F\u3081\u3001\u5727\u529B\u5DEE\u304C\u306A\u3051\u308C\u3070\u5E73\u9762\u3068\u306A\u308B\u3002\u3057\u305F\u304C\u3063\u3066\u754C\u9762\u306B\u66F2\u7387\u3092\u6301\u305F\u305B\u308B\u305F\u3081\u306B\u306F2\u76F8\u9593\u306B\u5727\u529B\u5DEE\u304C\u306A\u3051\u308C\u3070\u306A\u3089\u306A\u3044\u3002 \u30E9\u30D7\u30E9\u30B9\u5727\u3092\u0394p := pliquid - pgas\u3068\u5B9A\u7FA9\u3059\u308B\u3068\u304D\u3001\u66F2\u7387\u306F\u754C\u9762\u304C\u6DB2\u76F8\u5074\u304B\u3089\u6C17\u76F8\u5074\u306B\u5411\u304B\u3063\u3066\u51F8\u306B\u66F2\u304C\u3063\u3066\u3044\u308B\u5834\u5408\u3092\u6B63\u3068\u3059\u308B\u3002\u305F\u3068\u3048\u3070\u6C17\u4F53\u4E2D\u306B\u7403\u5F62\u306E\u6DB2\u6EF4\u304C\u3042\u308B\u5834\u5408\u30012\u3064\u306E\u66F2\u7387\u306F\u3068\u3082\u306B\u6B63\u3067\u3042\u308A\u0394p > 0\u3001\u3059\u306A\u308F\u3061\u5727\u529B\u306F\u6DB2\u6EF4\u5185\u90E8\u306E\u307B\u3046\u304C\u5927\u304D\u3044\u3002\u978D\u70B9\u306E\u3088\u3046\u306B2\u3064\u306E\u66F2\u7387\u304C\u7570\u7B26\u53F7\u3067\u3042\u308B\u5834\u5408\u3001\u754C\u9762\u5185\u5916\u306E\u3069\u3061\u3089\u306E\u5727\u529B\u304C\u5927\u304D\u3044\u304B\u306FR1, R2\u306B\u3088\u308B\u3002 2\u3064\u306E\u66F2\u7387\u306F\u4E3B\u66F2\u7387\u306B\u3068\u3089\u308C\u308B\u3053\u3068\u304C\u591A\u3044\u304C\u3001\u4EFB\u610F\u306E\u76F4\u4EA4\u3059\u308B\u3001\u754C\u9762\u306E\u6CD5\u7DDA\u30D9\u30AF\u30C8\u30EB\u3092\u542B\u30802\u5E73\u9762\u306B\u5BFE\u3057\u3066\u3068\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u3053\u308C\u306F\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u3088\u308A\u30012\u3064\u306E\u66F2\u7387\u534A\u5F84\u304C\u4E92\u3044\u306B\u76F4\u4EA4\u3059\u308B\u9762\u306B\u5BFE\u3057\u3066\u6C7A\u5B9A\u3055\u308C\u3066\u3044\u308C\u30701/R1 + 1/R2\u306E\u5024\u306F\u4E00\u5B9A\u3067\u3042\u308B\u3053\u3068\u304C\u793A\u3055\u308C\u3066\u3044\u308B\u305F\u3081\u3067\u3042\u308B\u3002 \u540D\u79F0\u306F\u30C8\u30DE\u30B9\u30FB\u30E4\u30F3\u30B0\u3068\u30D4\u30A8\u30FC\u30EB\uFF1D\u30B7\u30E2\u30F3\u30FB\u30E9\u30D7\u30E9\u30B9\u306B\u3061\u306A\u3080\u3002"@ja . . . . . "A liquid bridge is produced for an over pressure of \u0394p*=3.5 and initial condition r0=0.25\u22124, z0=0, dz/dr=0"@en . . . . . "\u30E4\u30F3\u30B0\u30FB\u30E9\u30D7\u30E9\u30B9\u306E\u5F0F\u3068\u306F\u3001\u66F2\u7387\u3092\u3082\u3064\u6C17\u76F8\u30FB\u6DB2\u76F8\u306E\u754C\u9762\u306B\u304A\u3044\u3066\u30012\u76F8\u9593\u306E\u5727\u529B\u5DEE\u3068\u754C\u9762\u306E\u66F2\u7387\u3092\u95A2\u9023\u4ED8\u3051\u308B\u65B9\u7A0B\u5F0F\u3067\u3042\u308B\u3002\u8868\u9762\u5F35\u529B\u3092\u03B3\u3001\u754C\u9762\u306E2\u3064\u306E\u66F2\u7387\u534A\u5F84\u3092R1, R2\u3068\u3059\u308B\u3068\u3001\u5727\u529B\u5DEE\u0394p\uFF08\u30E9\u30D7\u30E9\u30B9\u5727\u3082\u3057\u304F\u306F\u6BDB\u7BA1\u5727\u3068\u547C\u3070\u308C\u308B\uFF09\u306F\u6B21\u5F0F\u3067\u8868\u3055\u308C\u308B\uFF1A \u8868\u9762\u5F35\u529B\u306F\u754C\u9762\u3092\u6700\u5C0F\u5316\u3059\u308B\u3088\u3046\u306B\u306F\u305F\u3089\u304F\u305F\u3081\u3001\u5727\u529B\u5DEE\u304C\u306A\u3051\u308C\u3070\u5E73\u9762\u3068\u306A\u308B\u3002\u3057\u305F\u304C\u3063\u3066\u754C\u9762\u306B\u66F2\u7387\u3092\u6301\u305F\u305B\u308B\u305F\u3081\u306B\u306F2\u76F8\u9593\u306B\u5727\u529B\u5DEE\u304C\u306A\u3051\u308C\u3070\u306A\u3089\u306A\u3044\u3002 \u30E9\u30D7\u30E9\u30B9\u5727\u3092\u0394p := pliquid - pgas\u3068\u5B9A\u7FA9\u3059\u308B\u3068\u304D\u3001\u66F2\u7387\u306F\u754C\u9762\u304C\u6DB2\u76F8\u5074\u304B\u3089\u6C17\u76F8\u5074\u306B\u5411\u304B\u3063\u3066\u51F8\u306B\u66F2\u304C\u3063\u3066\u3044\u308B\u5834\u5408\u3092\u6B63\u3068\u3059\u308B\u3002\u305F\u3068\u3048\u3070\u6C17\u4F53\u4E2D\u306B\u7403\u5F62\u306E\u6DB2\u6EF4\u304C\u3042\u308B\u5834\u5408\u30012\u3064\u306E\u66F2\u7387\u306F\u3068\u3082\u306B\u6B63\u3067\u3042\u308A\u0394p > 0\u3001\u3059\u306A\u308F\u3061\u5727\u529B\u306F\u6DB2\u6EF4\u5185\u90E8\u306E\u307B\u3046\u304C\u5927\u304D\u3044\u3002\u978D\u70B9\u306E\u3088\u3046\u306B2\u3064\u306E\u66F2\u7387\u304C\u7570\u7B26\u53F7\u3067\u3042\u308B\u5834\u5408\u3001\u754C\u9762\u5185\u5916\u306E\u3069\u3061\u3089\u306E\u5727\u529B\u304C\u5927\u304D\u3044\u304B\u306FR1, R2\u306B\u3088\u308B\u3002 2\u3064\u306E\u66F2\u7387\u306F\u4E3B\u66F2\u7387\u306B\u3068\u3089\u308C\u308B\u3053\u3068\u304C\u591A\u3044\u304C\u3001\u4EFB\u610F\u306E\u76F4\u4EA4\u3059\u308B\u3001\u754C\u9762\u306E\u6CD5\u7DDA\u30D9\u30AF\u30C8\u30EB\u3092\u542B\u30802\u5E73\u9762\u306B\u5BFE\u3057\u3066\u3068\u308B\u3053\u3068\u304C\u3067\u304D\u308B\u3002\u3053\u308C\u306F\u5FAE\u5206\u5E7E\u4F55\u5B66\u306B\u3088\u308A\u30012\u3064\u306E\u66F2\u7387\u534A\u5F84\u304C\u4E92\u3044\u306B\u76F4\u4EA4\u3059\u308B\u9762\u306B\u5BFE\u3057\u3066\u6C7A\u5B9A\u3055\u308C\u3066\u3044\u308C\u30701/R1 + 1/R2\u306E\u5024\u306F\u4E00\u5B9A\u3067\u3042\u308B\u3053\u3068\u304C\u793A\u3055\u308C\u3066\u3044\u308B\u305F\u3081\u3067\u3042\u308B\u3002 \u540D\u79F0\u306F\u30C8\u30DE\u30B9\u30FB\u30E4\u30F3\u30B0\u3068\u30D4\u30A8\u30FC\u30EB\uFF1D\u30B7\u30E2\u30F3\u30FB\u30E9\u30D7\u30E9\u30B9\u306B\u3061\u306A\u3080\u3002"@ja . "La ley de Laplace es una ley f\u00EDsica que relaciona el cambio de presiones en la superficie que separa dos fluidos de distinta naturaleza con las fuerzas de l\u00EDnea debidas a efectos moleculares."@es . . . . "\u0417\u0430\u043A\u043E\u043D \u041B\u0430\u043F\u043B\u0430\u0441\u0430 \u2014 \u043F\u0440\u044F\u043C\u043E \u043F\u0440\u043E\u043F\u043E\u0440\u0446\u0456\u0439\u043D\u0430 \u0437\u0430\u043B\u0435\u0436\u043D\u0456\u0441\u0442\u044C \u043A\u0430\u043F\u0456\u043B\u044F\u0440\u043D\u043E\u0433\u043E \u0442\u0438\u0441\u043A\u0443 \u0432\u0456\u0434 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0435\u0432\u043E\u0433\u043E \u043D\u0430\u0442\u044F\u0433\u0443 \u043D\u0430 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456 \u0440\u043E\u0437\u0434\u0456\u043B\u0443 \u0434\u0432\u043E\u0445 \u0440\u0456\u0434\u0438\u043D \u0430\u0431\u043E \u0440\u0456\u0434\u0438\u043D\u0438 \u0456 \u0433\u0430\u0437\u0443 \u0456 \u0432\u0456\u0434 \u0441\u0435\u0440\u0435\u0434\u043D\u044C\u043E\u0457 \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456 (\u0442\u043E\u0431\u0442\u043E .\u0422\u0443\u0442 \u0456 \u2014 \u0433\u043E\u043B\u043E\u0432\u043D\u0456 \u0440\u0430\u0434\u0456\u0443\u0441\u0438 \u043A\u0440\u0438\u0432\u0438\u043D\u0438 \u0434\u0432\u043E\u0445 \u0432\u0437\u0430\u0454\u043C\u043D\u043E \u043F\u0435\u0440\u043F\u0435\u043D\u0434\u0438\u043A\u0443\u043B\u044F\u0440\u043D\u0438\u0445 \u043D\u043E\u0440\u043C\u0430\u043B\u044C\u043D\u0438\u0445 \u043F\u0435\u0440\u0435\u0440\u0456\u0437\u0456\u0432 \u043F\u043E\u0432\u0435\u0440\u0445\u043D\u0456): \u0426\u0435\u0439 \u0437\u0430\u043A\u043E\u043D \u0454 \u043E\u0434\u043D\u0438\u043C \u0437 \u043E\u0441\u043D\u043E\u0432\u043D\u0438\u0445 \u0437\u0430\u043A\u043E\u043D\u0456\u0432 \u043A\u0430\u043F\u0456\u043B\u044F\u0440\u043D\u0438\u0445 \u044F\u0432\u0438\u0449. \u0419\u043E\u0433\u043E \u0432\u0456\u0434\u043A\u0440\u0438\u0432 \u041F. \u0421. \u041B\u0430\u043F\u043B\u0430\u0441 \u0432 1806 \u0440\u043E\u0446\u0456."@uk . . "1117497588"^^ . . . . "\u6768-\u62C9\u666E\u62C9\u65AF\u516C\u5F0F"@zh . "In physics, the Young\u2013Laplace equation (/l\u0259\u02C8pl\u0251\u02D0s/) is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin. The Young\u2013Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It's a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness):"@en . . "La legge di Laplace (o formula di Laplace) indica l'effetto della tensione superficiale tra due corpi di natura diversa. Considerando il caso elementare della bolla di sapone, si verifica un salto di pressione nell'attraversamento perpendicolare dato da: dove: \n* \u03B3 \u00E8 la tensione superficiale tra la superficie e l'esterno (ex: aria / sapone) \n* \u00E8 la somma delle curvature locali della superficie in esame, ed \u00E8 una propriet\u00E0 invariante della bolla stessa \n* delta p \u00E8 la differenza di pressione"@it . "In physics, the Young\u2013Laplace equation (/l\u0259\u02C8pl\u0251\u02D0s/) is an algebraic equation that describes the capillary pressure difference sustained across the interface between two static fluids, such as water and air, due to the phenomenon of surface tension or wall tension, although use of the latter is only applicable if assuming that the wall is very thin. The Young\u2013Laplace equation relates the pressure difference to the shape of the surface or wall and it is fundamentally important in the study of static capillary surfaces. It's a statement of normal stress balance for static fluids meeting at an interface, where the interface is treated as a surface (zero thickness): where is the Laplace pressure, the pressure difference across the fluid interface (the exterior pressure minus the interior pressure), is the surface tension (or wall tension), is the unit normal pointing out of the surface, is the mean curvature, and and are the principal radii of curvature. Note that only normal stress is considered, this is because it has been shown that a static interface is possible only in the absence of tangential stress. The equation is named after Thomas Young, who developed the qualitative theory of surface tension in 1805, and Pierre-Simon Laplace who completed the mathematical description in the following year. It is sometimes also called the Young\u2013Laplace\u2013Gauss equation, as Carl Friedrich Gauss unified the work of Young and Laplace in 1830, deriving both the differential equation and boundary conditions using Johann Bernoulli's virtual work principles."@en . . . "Pression de Laplace"@fr . "La legge di Laplace (o formula di Laplace) indica l'effetto della tensione superficiale tra due corpi di natura diversa. Considerando il caso elementare della bolla di sapone, si verifica un salto di pressione nell'attraversamento perpendicolare dato da: dove: \n* \u03B3 \u00E8 la tensione superficiale tra la superficie e l'esterno (ex: aria / sapone) \n* \u00E8 la somma delle curvature locali della superficie in esame, ed \u00E8 una propriet\u00E0 invariante della bolla stessa \n* delta p \u00E8 la differenza di pressione Questo salto di pressione (p1 > p2) determina l'esistenza del sistema \"bolla di sapone\" ed \u00E8 un tipico fenomeno che mostra l'effetto della tensione superficiale. Nel caso di superficie piana i due raggi di curvatura risultano pari a infinito, motivo per cui la differenza di pressione nel caso di superfici piane \u00E8 0. Nel caso della bolla di sapone la differenza di pressione risulta minore di zero. Mentre per un sistema opposto (goccia di acqua in aria) la differenza di pressione risulta maggiore di zero. Questo si spiega a causa del segno dei raggi osculatori, ricordando che il raggio osculatore \u00E8 positivo se si trova nella fase liquida, e minore di zero se si trova nella fase gas."@it . . . . . . . "A lei de Laplace (em honra ao f\u00EDsico e matem\u00E1tico franc\u00EAs Pierre Simon Laplace) as vezes chamada lei de Laplace-Young ou equa\u00E7\u00E3o de Young\u2013Laplace (por Thomas Young) \u00E9 uma lei da f\u00EDsica que relaciona a varia\u00E7\u00E3o de press\u00E3o na superf\u00EDcie que separa dois fluidos de distinta natureza com as for\u00E7as de liga\u00E7\u00E3o molecular. Em sua forma mais geral pode ser expressada como:"@pt . . . . . . . .