{"id":3041,"date":"2022-03-24T12:11:48","date_gmt":"2022-03-24T12:11:48","guid":{"rendered":"https:\/\/stage-wp.10minuteschool.com\/?p=3041"},"modified":"2022-03-24T06:19:24","modified_gmt":"2022-03-24T06:19:24","slug":"poissons-ratio","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/poissons-ratio\/","title":{"rendered":"\u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4, \u0987\u09b8\u09cd\u09aa\u09be\u09a4, \u09b0\u09ac\u09be\u09b0\u09c7\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995\u09a4\u09be, \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c0\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9"},"content":{"rendered":"

\u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 <\/b>(Poisson’s Ratio)<\/b><\/h2>\n

\u09af\u0996\u09a8 \u0995\u09cb\u09a8\u09cb \u09a4\u09be\u09b0\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u0996\u09a8 \u09a4\u09be\u09b0\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0995\u09bf\u099b\u09c1\u099f\u09be \u09ac\u09c7\u09a1\u09bc\u09c7 \u09af\u09be\u09af\u09bc \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09b8\u0999\u09cd\u0997\u09c7 \u09b8\u0999\u09cd\u0997\u09c7 \u09a4\u09be\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8 \u0995\u09bf\u099b\u09c1 \u0995\u09ae\u09c7 \u09af\u09be\u09af\u09bc \u09ac\u09be \u09a4\u09be\u09b0 \u09b8\u09b0\u09c1 \u09b9\u09af\u09bc\u09c7 \u09af\u09be\u09af\u09bc\u0964 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09af\u09c7 \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u09b9\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u09ac\u09b2\u09c7\u0964 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u0998\u099f\u09b2\u09c7 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u0993 \u0998\u099f\u09c7\u0964 <\/span>\u09ac\u09c8\u099c\u09cd\u099e\u09be\u09a8\u09bf\u0995 \u09b8\u09be\u0987\u09ae\u09a8 \u09aa\u09af\u09bc\u09b8\u09a8 \u09a6\u09c7\u0996\u09be\u09a8 \u09af\u09c7, \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964<\/b><\/p>\n

\u09b8\u0982\u099c\u09cd\u099e\u09be :<\/b> \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u0993 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u0964 \u098f \u09a7\u09cd\u09b0\u09c1\u09ac \u09b8\u0982\u0996\u09cd\u09af\u09be\u0995\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u0989\u09aa\u09be\u09a6\u09be\u09a8\u09c7\u09b0 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09ac\u09b2\u09c7\u0964 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u0995\u09c7 \u03c3<\/strong><\/span> \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09b9\u09af\u09bc\u0964<\/span><\/p>\n\\text { \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09aa\u09be\u09a4, } \\sigma=\\frac{\\text { \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf }}{\\text { \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf }}<\/span>\n

\u09ae\u09be\u09a8 :<\/b> \u09ac\u09c3\u09a4\u09cd\u09a4\u09be\u0995\u09be\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u0995\u09cb\u09a8\u09cb \u09a4\u09be\u09b0\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/span>L<\/span><\/span> \u0993 \u09ac\u09cd\u09af\u09be\u09b8 <\/span>D<\/span><\/span> \u09b9\u09b2\u09c7 \u098f\u09ac\u0982 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac\u09c7 \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf <\/span>l<\/span><\/span> \u09b9\u09b2\u09c7 \u0993 \u09ac\u09cd\u09af\u09be\u09b8 <\/span>d<\/span><\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0995\u09ae\u09c7 \u0997\u09c7\u09b2\u09c7, \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf =\\frac{l}{L}<\/span><\/span>\u00a0<\/span>\u098f\u09ac\u0982 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf =\\frac{d}{D}<\/span><\/span>\u00a0<\/span><\/p>\n

\u2234<\/span> \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4, \\sigma=\\frac{d \/ D}{l \/ L}=\\frac{d L}{D l}<\/span><\/span><\/p>\n

\u09ac\u09cd\u09af\u09be\u09b8\u09c7\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09c7 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09a6\u09bf\u09af\u09bc\u09c7\u0993 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u0995\u09c7 \u09aa\u09cd\u09b0\u0995\u09be\u09b6 \u0995\u09b0\u09be \u09af\u09c7\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964<\/span><\/p>\n

\"Poisson's<\/p>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u09a4\u09be\u09b0\u09c7\u09b0 \u0986\u09a6\u09bf \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/span>L<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 <\/span>r<\/span>\u0964 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09ac\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ad\u09be\u09ac\u09c7 \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf <\/span>\\Delta L<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 \u09b9\u09cd\u09b0\u09be\u09b8 <\/span>\\Delta r<\/span><\/span> \u09b9\u09b2\u09c7,<\/span><\/p>\n

\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf =\\frac{\\Delta L}{L_{0}}<\/span><\/span><\/p>\n

\u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf =-\\frac{\\Delta r}{r}<\/span><\/span><\/p>\n\\therefore \\sigma=\\frac{\\frac{\\Delta r}{r}}{\\frac{\\Delta L}{L_{0}}}=-\\frac{\\Delta r L_{0}}{r \\Delta L}<\/span>\n

\u098f\u0996\u09be\u09a8\u09c7 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u099a\u09bf\u09b9\u09cd\u09a8 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u09ac\u09cb\u099d\u09be\u09a8\u09cb \u09b9\u099a\u09cd\u099b\u09c7 \u09af\u09c7, \\Delta L<\/span><\/span> \u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09b2\u09c7 \\Delta r<\/span><\/span>\u00a0\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 <\/span>\\Delta L<\/span> <\/span>\u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09b2\u09c7 \\Delta r<\/span><\/span>\u00a0\u09a7\u09a8\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u09ac\u09c7\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09b2\u09c7 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09be\u09ac\u09c7 \u0986\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09c7\u09b2\u09c7 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09ac\u09c7\u0964<\/span><\/p>\n

\u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u098f\u0995\u0995 :<\/b> \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u098f\u0995\u0987 \u099c\u09be\u09a4\u09c0\u09af\u09bc \u09a6\u09c1\u099f\u09bf \u09b0\u09be\u09b6\u09bf\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09ac\u09b2\u09c7 \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u098f\u0995\u0995 \u09a8\u09c7\u0987\u0964 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09a6\u09c1\u099f\u09bf \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09ac\u09b2\u09c7 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u09ae\u09be\u09a4\u09cd\u09b0\u09be \u0993 \u098f\u0995\u0995 \u09a8\u09c7\u0987\u0964<\/span><\/p>\n

\u09a4\u09be\u09ce\u09aa\u09b0\u09cd\u09af :<\/b> \u0985\u09cd\u09af\u09be\u09b2\u09c1\u09ae\u09bf\u09a8\u09bf\u09af\u09bc\u09be\u09ae\u09c7\u09b0 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 <\/span>0.35<\/span> \u09ac\u09b2\u09a4\u09c7 \u09ac\u09cb\u099d\u09be\u09af\u09bc \u0985\u09cd\u09af\u09be\u09b2\u09c1\u09ae\u09bf\u09a8\u09bf\u09af\u09bc\u09be\u09ae\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09b0\u09be\u09ac\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09b2\u09c7 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u0993 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09bf\u0995\u09c3\u09a4\u09bf\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09b8\u09ac \u09b8\u09ae\u09af\u09bc <\/span>0.35<\/span> \u09b9\u09af\u09bc\u0964\u00a0<\/span><\/p>\n

\u09a4\u09be\u09a4\u09cd\u09a4\u09cd\u09ac\u09bf\u0995\u09ad\u09be\u09ac\u09c7 \u09a6\u09c7\u0996\u09be\u09a8\u09cb \u09af\u09be\u09af\u09bc \u09af\u09c7, <\/span>\u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u09ae\u09be\u09a8 <\/b>-1<\/span> \u098f\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u0995\u09ae \u098f\u09ac\u0982 <\/b>+\\frac{1}{2}<\/span><\/span>\u00a0\u098f\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be <\/b>\u0985\u09b0\u09cd\u09a5\u09be\u09ce -1 \\leq \\sigma \\leq \\frac{1}{2}<\/span><\/span>\u00a0\u0964 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac\u09c7 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u0995\u09c7\u09ac\u09b2\u09ae\u09be\u09a4\u09cd\u09b0 \u09a4\u0996\u09a8\u0987 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u0993\u09af\u09bc\u09be \u09b8\u09ae\u09cd\u09ad\u09ac \u09af\u0996\u09a8 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3\u09c7\u09b0 \u09ab\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ac\u09cd\u09af\u09be\u09b8 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09be\u09af\u09bc \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac\u09c0\u09af\u09bc \u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3 \u0998\u099f\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09be\u09b8\u09cd\u09a4\u09ac\u09c7 \u09a4\u09be \u0985\u09b8\u09ae\u09cd\u09ad\u09ac \u09a4\u09be\u0987 \u09ac\u09cd\u09af\u09ac\u09b9\u09be\u09b0\u09bf\u0995 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u09ae\u09be\u09a8 \u098b\u09a3\u09be\u09a4\u09cd\u09ae\u0995 \u09b9\u0993\u09af\u09bc\u09be \u09b8\u09ae\u09cd\u09ad\u09ac \u09a8\u09af\u09bc\u0964 \u09ac\u09c7\u09b6\u09bf\u09b0 \u09ad\u09be\u0997 \u09a7\u09be\u09a4\u09ac \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u098f \u09ae\u09be\u09a8 \u09b8\u09be\u09a7\u09be\u09b0\u09a3\u09a4 <\/span>0.3\u00a0<\/span>\u09b9\u09af\u09bc\u09c7 \u09a5\u09be\u0995\u09c7\u0964 \u09a7\u09be\u09a4\u09ac \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09c7 \u09a4\u09be\u0987 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u09b8\u09c0\u09ae\u09be \u09a7\u09b0\u09be \u09b9\u09af\u09bc 0 \\leq \\sigma \\leq \\frac{1}{2}<\/span><\/span>\u0964<\/span><\/p>\n

\u0987\u09b8\u09cd\u09aa\u09be\u09a4 \u09b0\u09ac\u09be\u09b0\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 <\/b>(Steel is more Elastic than Rubber)\u00a0<\/b><\/h2>\n

\u098f\u0995 \u099f\u09c1\u0995\u09b0\u09cb \u09b0\u09ac\u09be\u09b0\u09c7\u09b0 \u09ab\u09bf\u09a4\u09c7 \u099f\u09be\u09a8\u09b2\u09c7 \u09b8\u09b9\u099c\u09c7\u0987 \u09ac\u09c7\u09a1\u09bc\u09c7 \u09af\u09be\u09af\u09bc, \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u098f\u0995\u099f\u09bf \u0987\u09b8\u09cd\u09aa\u09be\u09a4\u09c7\u09b0 \u09a4\u09be\u09b0 \u099f\u09be\u09a8\u09b2\u09c7 \u09a4\u09be \u09b8\u09b9\u099c\u09c7 \u09ac\u09be\u09a1\u09bc\u09c7 \u09a8\u09be\u0964 \u098f\u0995\u0987 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u0993 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09a6\u09c1\u099f\u09bf \u09ad\u09bf\u09a8\u09cd\u09a8 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09af\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09a4\u09c7 \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09aa\u09cd\u09b0\u09a4\u09bf\u09b0\u09cb\u09a7 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u09b9\u09af\u09bc \u09b8\u09c7\u0987 \u09ac\u09b8\u09cd\u09a4\u09c1\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995\u09a4\u09be \u09a4\u09a4 \u09ac\u09c7\u09b6\u09bf\u0964 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b0\u09cb\u09a7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09c1\u0995\u09cd\u09a4 \u09ac\u09b2\u09c7\u09b0 \u09b8\u09ae\u09be\u09a8 \u09ac\u09b2\u09c7 \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09a4\u09c7 \u09af\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1\u09a4\u09c7 \u09af\u09a4 \u09ac\u09c7\u09b6\u09bf \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09a4\u09a4 \u09ac\u09c7\u09b6\u09bf \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09b2\u09be \u09b9\u09af\u09bc\u0964 \u098f \u09b9\u09bf\u09b8\u09be\u09ac\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, \u098f\u0995\u0987 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0993 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u09b0\u09ac\u09be\u09b0 \u0993 \u0987\u09b8\u09cd\u09aa\u09be\u09a4\u09c7\u09b0 \u09a4\u09be\u09b0\u09c7 \u09b8\u09ae\u09be\u09a8 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u0995\u09b0\u09a4\u09c7 \u09b0\u09ac\u09be\u09b0\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0987\u09b8\u09cd\u09aa\u09be\u09a4\u09c7\u09b0 \u09a4\u09be\u09b0\u09c7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc \u0985\u09a8\u09c7\u0995 \u09ac\u09c7\u09b6\u09bf\u0964 \u098f\u099c\u09a8\u09cd\u09af \u09b0\u09ac\u09be\u09b0\u09c7\u09b0 \u09a4\u09c1\u09b2\u09a8\u09be\u09af\u09bc \u0987\u09b8\u09cd\u09aa\u09be\u09a4\u09c7\u09b0 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995\u09a4\u09be \u0985\u09a8\u09c7\u0995 \u09ac\u09c7\u09b6\u09bf\u0964<\/span><\/p>\n

\"Poisson's<\/p>\n

\u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995 \u0993 \u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4\u09c7\u09b0 \u09a4\u09be\u09b2\u09bf\u0995\u09be<\/b><\/h3>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
<\/td>\n\u09aa\u09a6\u09be\u09b0\u09cd\u09a5<\/b><\/td>\n\u0987\u09df\u0982 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995<\/b><\/p>\n

10^{10}\u00a0N\u00a0m^{-2}<\/span><\/td>\n

\u0986\u09df\u09a4\u09a8 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995<\/b><\/p>\n

10^{10}\u00a0N\u00a0m^{-2}<\/span><\/td>\n

\u09a6\u09c3\u09dd\u09a4\u09be\u09b0 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995<\/b><\/p>\n

10^{10}\u00a0N\u00a0m{-2}<\/span><\/td>\n

\u09aa\u09df\u09b8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4<\/b><\/td>\n<\/tr>\n
\u09e7<\/span><\/td>\n\u0987\u09b8\u09cd\u09aa\u09be\u09a4<\/span><\/td>\n20<\/span><\/td>\n17<\/span><\/td>\n8.4<\/span><\/td>\n0.33<\/span><\/td>\n<\/tr>\n
\u09e8<\/span><\/td>\n\u09b2\u09cb\u09b9\u09be (\u09aa\u09c7\u099f\u09be)<\/span><\/td>\n20<\/span><\/td>\n17<\/span><\/td>\n8.0<\/span><\/td>\n0.28<\/span><\/td>\n<\/tr>\n
\u09e9<\/span><\/td>\n\u09a8\u09bf\u0995\u09c7\u09b2<\/span><\/td>\n20<\/span><\/td>\n16<\/span><\/td>\n7.9<\/span><\/td>\n0.31<\/span><\/td>\n<\/tr>\n
\u09ea<\/span><\/td>\n\u09a4\u09be\u09ae\u09be<\/span><\/td>\n13<\/span><\/td>\n14<\/span><\/td>\n4.8<\/span><\/td>\n0.34<\/span><\/td>\n<\/tr>\n
\u09eb<\/span><\/td>\n\u09b2\u09cb\u09b9\u09be (\u09a2\u09be\u09b2\u09be\u0987)<\/span><\/td>\n11.5<\/span><\/td>\n90<\/span><\/td>\n4.6<\/span><\/td>\n0.24<\/span><\/td>\n<\/tr>\n
\u09ec<\/span><\/td>\n\u09aa\u09bf\u09a4\u09b2 (<\/span>60%<\/span> \u09a4\u09be\u09ae\u09be)<\/span><\/td>\n10<\/span><\/td>\n11<\/span><\/td>\n3.5<\/span><\/td>\n0.33<\/span><\/td>\n<\/tr>\n
\u09ed<\/span><\/td>\n\u0985\u09cd\u09af\u09be\u09b2\u09c1\u09ae\u09bf\u09a8\u09bf\u09df\u09be\u09ae<\/span><\/td>\n7.00<\/span><\/td>\n7.7<\/span><\/td>\n2.6<\/span><\/td>\n0.35<\/span><\/td>\n<\/tr>\n
\u09ee<\/span><\/td>\n\u0995\u09be\u0981\u099a<\/span><\/td>\n6.00<\/span><\/td>\n3.7<\/span><\/td>\n3.1<\/span><\/td>\n0.18-0.3<\/span><\/td>\n<\/tr>\n
\u09ef<\/span><\/td>\n\u09b8\u09c0\u09b8\u09be<\/span><\/td>\n1.6<\/span><\/td>\n4.6<\/span><\/td>\n0.56<\/span><\/td>\n0.44<\/span><\/td>\n<\/tr>\n
\u09e7\u09e6<\/span><\/td>\n\u09aa\u09be\u09b0\u09a6<\/span><\/td>\n<\/td>\n2.8<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\u09e7\u09e7<\/span><\/td>\n\u0997\u09cd\u09b2\u09bf\u09b8\u09be\u09b0\u09bf\u09a8<\/span><\/td>\n<\/td>\n0.40<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\u09e7\u09e8<\/span><\/td>\n\u09aa\u09be\u09a8\u09bf<\/span><\/td>\n<\/td>\n0.21<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\u09e7\u09e9<\/span><\/td>\n\u09aa\u09c7\u099f\u09cd\u09b0\u09cb\u09b2\u09bf\u09df\u09be\u09ae<\/span><\/td>\n<\/td>\n0.14<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n
\u09e7\u09ea<\/span><\/td>\n\u0987\u09a5\u09be\u0987\u09b2 \u0985\u09cd\u09af\u09be\u09b2\u0995\u09cb\u09b9\u09b2<\/span><\/td>\n<\/td>\n0.11<\/span><\/td>\n<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u00a0<\/span><\/p>\n

\u09b8\u09ae\u09cd\u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09bf\u09a4 \u0995\u09b0\u09cd\u09ae\u0995\u09be\u09a3\u09cd\u09a1 <\/b>(Extended Activities)<\/b><\/h3>\n

\u09a4\u09be\u09b0\u09c7\u09b0 \u09b8\u09ae\u09cd\u09aa\u09cd\u09b0\u09b8\u09be\u09b0\u09a3\u09c7 \u0995\u09c3\u09a4\u0995\u09be\u099c \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be \u09ac\u09c7\u09b0 \u0995\u09b0\u0964\u00a0<\/b><\/p>\n

\u09ac\u09be\u0987\u09b0\u09c7 \u09a5\u09c7\u0995\u09c7 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09c7 \u0995\u09cb\u09a8\u09cb \u09ac\u09b8\u09cd\u09a4\u09c1\u0995\u09c7 \u09ac\u09bf\u0995\u09c3\u09a4 \u0995\u09b0\u09b2\u09c7 \u0995\u09bf\u099b\u09c1 \u0995\u09be\u099c \u0995\u09b0\u09a4\u09c7 \u09b9\u09af\u09bc \u098f\u09ac\u0982 \u0990 \u0995\u09be\u099c \u09ac\u09b8\u09cd\u09a4\u09c1\u09a4\u09c7 \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf\u09b0\u09c2\u09aa\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09a5\u09be\u0995\u09c7\u0964 \u0986\u09ac\u09be\u09b0 \u09ac\u09be\u09b9\u09cd\u09af\u09bf\u0995 \u09ac\u09b2 \u0985\u09aa\u09b8\u09be\u09b0\u09bf\u09a4 \u09b9\u09b2\u09c7 \u09ac\u09b8\u09cd\u09a4\u09c1 \u09a4\u09be\u09b0 \u0986\u0997\u09c7\u09b0 \u0986\u0995\u09be\u09b0 \u09ab\u09bf\u09b0\u09c7 \u09aa\u09be\u09af\u09bc \u098f\u09ac\u0982 \u0990 \u09b6\u0995\u09cd\u09a4\u09bf \u09a4\u09be\u09aa\u09b6\u0995\u09cd\u09a4\u09bf\u09a4\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u09a4 \u09b9\u09df\u0964\u00a0<\/span><\/p>\n

\u09ae\u09cb\u099f \u0995\u09c3\u09a4\u0995\u09be\u099c \u09ac\u09be \u09ac\u09bf\u09ad\u09ac \u09ac\u09be \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf \u09b6\u0995\u09cd\u09a4\u09bf <\/b>(Total Accomplishment or Potental or Status Energy)\u00a0<\/b><\/h3>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, <\/span>L<\/span><\/span> \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0993 <\/span>A<\/span><\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2\u09ac\u09bf\u09b6\u09bf\u09b7\u09cd\u099f \u098f\u0995\u099f\u09bf \u09a4\u09be\u09b0\u0995\u09c7 \u09a6\u09c3\u09a2\u09bc \u0985\u09ac\u09b2\u09ae\u09cd\u09ac\u09a8 \u09a5\u09c7\u0995\u09c7 \u099d\u09c1\u09b2\u09be\u09a8\u09cb \u09b9\u09af\u09bc\u09c7\u099b\u09c7\u0964 \u09ae\u09a8\u09c7 \u0995\u09b0\u09bf, \u098f\u0987 \u09a4\u09be\u09b0\u09c7 <\/span>F<\/span><\/span> \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09be\u09b0 \u09ab\u09b2\u09c7 \u098f\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/span>dl<\/span> <\/span>\u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf \u09aa\u09c7\u09b2\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a4\u09be\u09b0\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf\u09b0 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 \u09ac\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c \u09b9\u09ac\u09c7 <\/span>=<\/span> \u09ac\u09b2 <\/span> \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf\u0964<\/span><\/p>\n

\u0995\u09c3\u09a4\u0995\u09be\u099c <\/span>d W=F d l<\/span><\/span><\/p>\n

\u098f\u0987 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u0995\u09c7 <\/span>l=\u00a00<\/span> <\/span>\u09a5\u09c7\u0995\u09c7 <\/span>l=l<\/span>\u00a0<\/span> \u098f\u0987 \u09b8\u09c0\u09ae\u09be\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09ae\u09be\u0995\u09b2\u09a8 \u0995\u09b0\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09ae\u09cb\u099f \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c \u09aa\u09be\u0987,<\/span><\/p>\n

W=\\int_{0}^{l} F d l<\/span>\u00a0 <\/span>\u22ef\u22ef\u00a0 (7.15)<\/span><\/p>\n

\u0987\u09af\u09bc\u0982 \u0997\u09c1\u09a3\u09be\u0999\u09cd\u0995 \u09a5\u09c7\u0995\u09c7 \u0986\u09ae\u09b0\u09be \u099c\u09be\u09a8\u09bf \u09af\u09c7,<\/span><\/p>\nY=\\frac{F L}{A l}<\/span>\n

\u09af\u09c7\u0996\u09be\u09a8\u09c7 <\/span>L<\/span> \u09a4\u09be\u09b0\u09c7\u09b0 \u09ae\u09cb\u099f \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af, <\/span>A<\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u098f\u09ac\u0982 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c3\u09a6\u09cd\u09a7\u09bf, <\/span>F<\/span><\/span> \u09ac\u09b2\u0964<\/span><\/p>\nF=\\frac{Y A l}{L}<\/span>\n

\u098f\u0996\u09a8 <\/span>(7.15)<\/span> \u09b8\u09ae\u09c0\u0995\u09b0\u09a3\u09c7 <\/span>F<\/span> \u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09b8\u09be\u09b2\u09c7,<\/span><\/p>\nW=\\int_{0}^{l} \\frac{Y A l}{L} d l=\\frac{Y A}{L} \\int_{0}^{l} l d l=\\frac{Y A}{L}\\left[\\frac{l^{2}}{2}\\right]_{0}^{l}<\/span>\nW=\\frac{Y A}{L} \\frac{l^{2}}{2}<\/span>\n

W=\\frac{1}{2} \\frac{Y A l^{2}}{L}<\/span> \u2026 … \u2026\u00a0 <\/span>(7.16)<\/span><\/p>\n

\u098f\u0987 \u0995\u09be\u099c\u0987 \u09a4\u09be\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b8\u09cd\u09a5\u09bf\u09a4\u09bf\u09b8\u09cd\u09a5\u09be\u09aa\u0995 \u09ac\u09bf\u09ad\u09ac \u09b9\u09bf\u09b8\u09c7\u09ac\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09a5\u09be\u0995\u09c7\u0964\u00a0<\/span><\/p>\n

\u098f\u0995\u0995 \u0986\u09af\u09bc\u09a4\u09a8\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf <\/b>(The Potental Energy Stored in a Single Volume) <\/b>\u00a0<\/b><\/p>\n

\u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09a4\u09be\u09b0\u09c7\u09b0 \u09ae\u09cb\u099f \u0986\u09af\u09bc\u09a4\u09a8, <\/span>V=<\/span><\/span> \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u099a\u09cd\u099b\u09c7\u09a6\u09c7\u09b0 \u0995\u09cd\u09b7\u09c7\u09a4\u09cd\u09b0\u09ab\u09b2 \u00d7 <\/span> \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af <\/span>=\u00a0AL\u00a0<\/span><\/span><\/p>\n

\u098f\u0995\u0995 \u0986\u09af\u09bc\u09a4\u09a8\u09c7 \u09b8\u099e\u09cd\u099a\u09bf\u09a4 \u09ac\u09bf\u09ad\u09ac \u09b6\u0995\u09cd\u09a4\u09bf \u09ac\u09be \u0995\u09c3\u09a4\u0995\u09be\u099c\u00a0 U=\\frac{W}{V}<\/span><\/span><\/p>\n=\\frac{\\frac{1}{2} \\frac{Y A l^{2}}{L}}{A L}<\/span>\n=\\frac{1}{2} \\frac{Y A l}{L} \\frac{l}{L}=\\frac{1}{2} \\frac{Y l^{2}}{L^{2}}<\/span>\n

 <\/p>\n

\u2234U=\\frac{1}{2}<\/span><\/span> \u09aa\u09c0\u09a1\u09bc\u09a8 \u00d7 <\/span> \u09ac\u09bf\u0995\u09c3\u09a4\u09bf<\/span><\/p>\n

\u0995\u09be\u09b0\u09a3 \u09aa\u09c0\u09a1\u09bc\u09a8 =\\frac{F}{A}=\\frac{Yl}{L}<\/span><\/span> \u098f\u09ac\u0982 \u09ac\u09bf\u0995\u09c3\u09a4\u09bf =\\frac{l}{L}<\/span><\/span><\/p>\n

\u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c0\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 <\/b>(Flow of Fluids)\u00a0<\/b><\/h2>\n

\u09b8\u09cd\u09b0\u09cb\u09a4\u09b0\u09c7\u0996\u09be \u09ac\u09be \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 <\/b>(Streamline flow)<\/b><\/h3>\n

\u09ae\u09a8\u09c7 \u0995\u09b0\u09be \u09af\u09be\u0995, <\/span>\\mathrm{ABC}<\/span><\/span> \u09aa\u09a5 \u09ac\u09b0\u09be\u09ac\u09b0 \u0995\u09cb\u09a8\u09cb \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u099a\u09cd\u099b\u09c7\u0964 \u09a7\u09b0\u09be \u09af\u09be\u0995 \u09af\u09c7, \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be \\overrightarrow{\\mathrm{v}_{1}}, \\overrightarrow{\\mathrm{v}_{2}}<\/span><\/span> \u098f\u09ac\u0982 \\overrightarrow{\\mathrm{v}_{3}}<\/span><\/span> \u09ac\u09c7\u0997 \u09a8\u09bf\u09af\u09bc\u09c7 \u09af\u09a5\u09be\u0995\u09cd\u09b0\u09ae\u09c7 \\mathrm{A}, \\mathrm{B}<\/span><\/span>\u00a0\u0993 <\/span>\\mathrm{C}<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae \u0995\u09b0\u099b\u09c7\u0964 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u099f\u09bf \u09af\u09a6\u09bf \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7 \u0995\u09cb\u09a8\u09cb \u09a8\u09a4\u09c1\u09a8 \u0995\u09a3\u09be <\/span>\\mathrm{A}<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09aa\u09cc\u099b\u09be\u09b2\u09c7 \u098f\u09b0 \u09ac\u09c7\u0997 \\overrightarrow{\\mathrm{v}_{1}}<\/span><\/span>\u00a0\u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09ac\u09c7\u0964 \u098f \u09ac\u09c7\u0997\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u09b9\u09ac\u09c7 \\mathrm{A}<\/span><\/span>\u00a0\u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 <\/span>\\mathrm{ABC}<\/span><\/span> \u09aa\u09a5\u09c7\u09b0 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996\u09c7\u0964 \u0995\u09cb\u09a8\u09cb \u0995\u09a3\u09be \\mathrm{B}<\/span><\/span> \u09a4\u09c7 \u09aa\u09cc\u0981\u099b\u09be\u09b2\u09c7 \u098f\u09b0 \u09ac\u09c7\u0997 \u09b9\u09ac\u09c7 \\overrightarrow{\\mathrm{v}_{2}}<\/span><\/span>\u0964 \u098f\u0987 \u09ac\u09c7\u0997 \\overrightarrow{\\mathrm{v}_{1}}<\/span><\/span> \u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u0986\u09ac\u09be\u09b0 \u09a8\u09be\u0993 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u098f\u0995\u0987\u09ad\u09be\u09ac\u09c7 \\mathrm{C}<\/span><\/span> \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae\u0995\u09be\u09b0\u09c0 \u09b8\u0995\u09b2 \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997 \u09b9\u09ac\u09c7 \\overrightarrow{\\mathrm{v}_{3}}<\/span><\/span>\u0964 <\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09ac\u09b2\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7, <\/span>\u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u0993\u09af\u09bc\u09be\u09b0 \u09b8\u09ae\u09af\u09bc \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u09b8\u0995\u09b2 \u0995\u09a3\u09be \u09af\u09a6\u09bf \u098f\u0995\u0987 \u09ac\u09c7\u0997 \u09a8\u09bf\u09af\u09bc\u09c7 \u098f\u09b0 \u0985\u0997\u09cd\u09b0\u09ac\u09b0\u09cd\u09a4\u09c0 \u0995\u09a3\u09be\u09b0 \u09aa\u09a5 \u0985\u09a8\u09c1\u09b8\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a4\u09be\u09b9\u09b2\u09c7 \u09b8\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u0995\u09c7 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09ac\u09be \u09b8\u09cd\u09b0\u09cb\u09a4\u09b0\u09c7\u0996\u09be \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09ac\u09be \u09b6\u09be\u09a8\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09ac\u09b2\u09c7\u0964<\/b> \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c7\u09b0 \u09ac\u09c7\u09b2\u09be\u09af\u09bc \u0995\u09cb\u09a8\u09cb \u09a8\u09bf\u09b0\u09cd\u09a6\u09bf\u09b7\u09cd\u099f \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u0985\u09a4\u09bf\u0995\u09cd\u09b0\u09ae\u0995\u09be\u09b0\u09c0 \u09b8\u0995\u09b2 \u0995\u09a3\u09be\u09b0 \u0990 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09ac\u09c7\u0997 \u098f\u0995\u0987 \u09ac\u09be \u09b8\u09ae\u09be\u09a8 \u09a5\u09be\u0995\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u0995\u09a3\u09be\u0997\u09c1\u09b2\u09cb\u09b0 \u09ac\u09c7\u0997 \u098f\u09a6\u09c7\u09b0 \u09aa\u09a5\u09c7\u09b0 \u09ac\u09bf\u09ad\u09bf\u09a8\u09cd\u09a8 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09aa\u09c3\u09a5\u0995 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u0986\u09ac\u09be\u09b0 \u09a8\u09be\u0993 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09b9\u09b2\u09c7 \u0997\u09a4\u09bf\u09aa\u09a5\u09c7\u09b0 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u0985\u0999\u09cd\u0995\u09bf\u09a4 \u09b8\u09cd\u09aa\u09b0\u09cd\u09b6\u0995 \u0990 \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09b0\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c7\u09b0 \u0985\u09ad\u09bf\u09ae\u09c1\u0996 \u09ac\u09be \u09a6\u09bf\u0995 \u09a8\u09bf\u09b0\u09cd\u09a6\u09c7\u09b6 \u0995\u09b0\u09c7\u0964 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996\u09be \u09b8\u09b0\u09b2 \u09ac\u09be \u09ac\u0995\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7\u0964\u00a0<\/span><\/p>\n

\u098f\u0995\u0997\u09c1\u099a\u09cd\u099b \u09a7\u09be\u09b0\u09be \u09b0\u09c7\u0996\u0995\u09c7 \u098f\u0995\u09a4\u09cd\u09b0\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09a8\u09b2 \u09ac\u09be \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09ac\u09b2\u09c7\u0964<\/span><\/p>\n

\"Poisson's<\/p>\n

\u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 <\/b>(Turbulent flow)<\/b><\/h3>\n

\u0995\u09cb\u09a8\u09cb \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u09af\u09bc \u09af\u09a6\u09bf \u098f\u09b0 \u09ac\u09c7\u0997 <\/span>\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf \u09ac\u09c7\u0997 <\/b>\u09a8\u09be\u09ae\u0995 \u098f\u0995\u099f\u09bf \u09b8\u09c0\u09ae\u09be\u09a8\u09cd\u09a4\u09bf\u0995 \u09ac\u09c7\u0997\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u0995\u09ae \u09b9\u09af\u09bc\u0964 \u0995\u09cb\u09a8\u09cb \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u09ac\u09c7\u0997 \u09af\u09a6\u09bf \u098f\u09b0 \u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf \u09ac\u09c7\u0997\u09c7\u09b0 \u099a\u09c7\u09af\u09bc\u09c7 \u09ac\u09c7\u09b6\u09bf \u09b9\u09af\u09bc \u09a4\u09be\u09b9\u09b2\u09c7 \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u0995\u09a3\u09be\u09b0 \u09aa\u09a5 \u0993 \u09ac\u09c7\u0997 \u09aa\u09cd\u09b0\u09a4\u09bf\u09a8\u09bf\u09af\u09bc\u09a4 \u098f\u09b2\u09cb\u09ae\u09c7\u09b2\u09cb\u09ad\u09be\u09ac\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc \u09ab\u09b2\u09c7 \u0995\u09a3\u09be\u0997\u09c1\u09b2\u09cb \u0986\u0981\u0995\u09be\u09ac\u09be\u0981\u0995\u09be \u09aa\u09a5\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u09af\u09bc\u0964 \u098f\u09a4\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c0 \u098f\u09b0 \u09b8\u0995\u09b2 \u09a8\u09bf\u09af\u09bc\u09ae\u09be\u09a8\u09c1\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4\u09be \u09b9\u09be\u09b0\u09bf\u09af\u09bc\u09c7 \u09ab\u09c7\u09b2\u09c7\u0964 <\/span>\u098f \u09a7\u09b0\u09a8\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u0995\u09c7 \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09ac\u09be \u0985\u09a8\u09bf\u09af\u09bc\u09a4 \u09ac\u09be \u0985\u09b6\u09be\u09a8\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09ac\u09b2\u09c7\u0964 \u098f \u09a7\u09b0\u09a8\u09c7\u09b0 \u0997\u09a4\u09bf\u09a4\u09c7 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09a4\u09c7 \u09a4\u09b0\u09b2 \u09aa\u09a6\u09be\u09b0\u09cd\u09a5\u09c7\u09b0 \u0995\u09a3\u09be\u09b0 \u09ac\u09c7\u0997\u09c7\u09b0 \u09ae\u09be\u09a8 \u0993 \u09a6\u09bf\u0995 \u0989\u09ad\u09af\u09bc\u0987 \u09b8\u09ae\u09af\u09bc\u09c7\u09b0 \u09b8\u09be\u09a5\u09c7 \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09b9\u09af\u09bc\u0964<\/span><\/p>\n

\"Poisson's<\/h4>\n

\u0985\u09a7\u09cd\u09af\u09be\u09aa\u0995 <\/span>\u0985\u09b8\u09ac\u09b0\u09cd\u09a8 \u09b0\u09c7\u09a8\u09b2\u09cd\u09a1\u09b8 <\/b>(Prof. Osborne Reynolds)<\/span> \u09b8\u09b0\u09cd\u09ac\u09aa\u09cd\u09b0\u09a5\u09ae \u09aa\u09cd\u09b0\u09ae\u09be\u09a3 \u0995\u09b0\u09c7\u09a8 \u09af\u09c7, \u0995\u09cb\u09a8\u09cb \u09a4\u09b0\u09b2\u09c7\u09b0 \u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf\u09ac\u09c7\u0997 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a4\u09b0\u09b2\u09c7\u09b0 \u09b8\u09be\u09a8\u09cd\u09a6\u09cd\u09b0\u09a4\u09be\u0999\u09cd\u0995 <\/span>(n)<\/span>, <\/span>\u09a4\u09b0\u09b2\u09c7\u09b0 \u0998\u09a8\u09a4\u09cd\u09ac (\\rho)<\/span><\/span> \u098f\u09ac\u0982 \u09af\u09c7 \u09a8\u09b2 \u09a6\u09bf\u09af\u09bc\u09c7 \u09a4\u09b0\u09b2 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09bf\u09a4 \u09b9\u099a\u09cd\u099b\u09c7 \u09a4\u09be\u09b0 \u09ac\u09cd\u09af\u09be\u09b8\u09be\u09b0\u09cd\u09a7\u09c7\u09b0 (r)<\/span><\/span>\u0989\u09aa\u09b0\u0964 \u09a4\u09bf\u09a8\u09bf \u09b9\u09bf\u09b8\u09be\u09ac \u0995\u09b0\u09c7 \u09a6\u09c7\u0996\u09be\u09a8 \u09af\u09c7,<\/span><\/h4>\n

\u0995\u09cd\u09b0\u09be\u09a8\u09cd\u09a4\u09bf\u09ac\u09c7\u0997, v_{c} \\propto \\frac{n}{\\rho r}<\/span><\/span><\/p>\nv_{c}=R_{e} \\frac{n}{\\rho r}<\/span>\n

\u098f\u0996\u09be\u09a8\u09c7, R_{e}=<\/span><\/span>\u00a0\u09b0\u09c7\u09a8\u09b2\u09cd\u09a1\u09b8-\u098f\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>=<\/span> \u098f\u0995\u099f\u09bf \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u0964 \u098f\u0987 \u09a7\u09cd\u09b0\u09c1\u09ac\u0995\u09c7\u09b0 \u09ae\u09be\u09a8\u09c7\u09b0 \u0989\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a4\u09b0\u09b2\u09c7\u09b0 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09b9\u09ac\u09c7 \u09a8\u09be \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09b9\u09ac\u09c7\u0964 R_{e}<2000<\/span><\/span>\u00a0\u09b9\u09b2\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b0\u09c7\u09a8\u09b2\u09cd\u09a1\u09b8-\u098f\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be <\/span>2000<\/span>-\u098f\u09b0 \u0995\u09ae \u09b9\u09b2\u09c7 \u09a4\u09b0\u09b2 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09b9\u09ac\u09c7\u0964 \u0986\u09b0 R_{e}<\/span><\/span>\u00a0\u098f\u09b0 \u09ae\u09be\u09a8 <\/span>2000<\/span> \u09a5\u09c7\u0995\u09c7 <\/span>3000<\/span> \u098f\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09b9\u09b2\u09c7 \u09ac\u09c1\u099d\u09a4\u09c7 \u09b9\u09ac\u09c7 \u09a4\u09b0\u09b2 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09a7\u09be\u09b0\u09be\u09b0\u09c7\u0996 \u09a5\u09c7\u0995\u09c7 \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c7 \u09b0\u09c2\u09aa\u09be\u09a8\u09cd\u09a4\u09b0\u09bf\u09a4 \u09b9\u099a\u09cd\u099b\u09c7\u0964 R_{e}<\/span><\/span>\u00a0\u098f\u09b0 \u09ae\u09be\u09a8 <\/span>3000<\/span> \u098f\u09b0 \u0989\u09aa\u09b0\u09c7 \u09b9\u09b2\u09c7 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9 \u09aa\u09c1\u09b0\u09cb\u09aa\u09c1\u09b0\u09bf \u09ac\u09bf\u0995\u09cd\u09b7\u09bf\u09aa\u09cd\u09a4 \u09aa\u09cd\u09b0\u09ac\u09be\u09b9\u09c7 \u09aa\u09b0\u09bf\u09a3\u09a4 \u09b9\u09ac\u09c7\u0964\u00a0<\/span><\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

\u09aa\u09af\u09bc\u09b8\u09a8\u09c7\u09b0 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 (Poisson’s Ratio) \u09af\u0996\u09a8 \u0995\u09cb\u09a8\u09cb \u09a4\u09be\u09b0\u09c7 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09b0\u09be\u09ac\u09b0 \u09ac\u09b2 \u09aa\u09cd\u09b0\u09af\u09bc\u09cb\u0997 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u0996\u09a8 \u09a4\u09be\u09b0\u09c7\u09b0 \u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u0995\u09bf\u099b\u09c1\u099f\u09be \u09ac\u09c7\u09a1\u09bc\u09c7 \u09af\u09be\u09af\u09bc \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09b8\u0999\u09cd\u0997\u09c7 \u09b8\u0999\u09cd\u0997\u09c7 \u09a4\u09be\u09b0\u09c7\u09b0 \u09ac\u09cd\u09af\u09be\u09b8 \u0995\u09bf\u099b\u09c1 \u0995\u09ae\u09c7 \u09af\u09be\u09af\u09bc \u09ac\u09be \u09a4\u09be\u09b0 \u09b8\u09b0\u09c1 \u09b9\u09af\u09bc\u09c7 \u09af\u09be\u09af\u09bc\u0964 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0 \u09a6\u09bf\u0995\u09c7 \u09af\u09c7 \u09ac\u09bf\u0995\u09c3\u09a4\u09bf \u09b9\u09af\u09bc \u09a4\u09be\u0995\u09c7 \u09aa\u09be\u09b0\u09cd\u09b6\u09cd\u09ac \u09ac\u09bf\u0995\u09c3\u09a4\u09bf<\/p>\n

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