Mathematic Methods HW Solutions 68

Mathematic Methods HW Solutions 68 - Chapter 14 68 10.4 T =...

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Chapter 14 68 10.4 T = 200 π - 1 arc tan( y/x ) 10.5 V = 200 π - 1 arc tan( y/x ) 10.6 T = 100 y/ ( x 2 + y 2 ); isothermals y/ ( x 2 + y 2 ) = const.; fow lines x/ ( x 2 + y 2 ) = const. 10.7 Streamlines xy = const.; Φ = ( x 2 - y 2 ) V 0 , Ψ = 2 xy V 0 , V = (2 i x - 2 j y ) V 0 10.9 Streamlines y - y/ ( x 2 + y 2 ) = const. 10.10 cos x sinh y = const. 10.11 ( x - coth u ) 2 + y 2 = csch 2 u x 2 + ( y + cot v ) 2 = csc 2 v 10.12 T = (20 ) arc tan[2 y/ (1 - x 2 - y 2 )], arc tan between π/ 2 and 3 π/ 2 10.13 V = V 2 - V 1 π arc tan 2 y 1 - x 2 - y 2 + 3 V 1 - V 2 2 , arc tan between π/ 2 and 3 π/ 2 10.14 φ = 1 2 V 0 ln ( x + 1) 2 + y 2 ( x - 1) 2 + y 2 ψ = V 0 arc tan 2 y 1 - x 2 - y 2 , arc tan between π/ 2 and 3 π/ 2 . V x = 2 V 0 (1 - x 2 + y 2 ) (1 - x 2 + y 2 ) 2 + 4 x 2 y 2 , V y = - 4 V 0 xy (1 - x 2 + y 2 ) 2 + 4 x 2 y 2 11.1 ln(1 + z ) 11.2 - i ln(1 + z ) 11.5 R ( i ) = (1 - i 3) / 4 11.6 R ( - 1 / 2) = i/ (6 2) R ( - i ) = - 1 / 2 R ( e iπ/ 3 / 2) = R ( e 5 πi/ 3 / 2) = - i/ (6 2) 11.7 R ( i ) = π/ 4, R ( - i ) = R ( e 3 πi/ 2 ) = - 3 π/ 4 11.8 R (1 / 2) = 1 / 2 11.9 - 1 / 6 11.10 - 1 11.12 1 / 2 11.13 (a) 1 / 96 (b) - 5 (c) - 1 / 80 (d) 1 / 2 11.14 (a) 2
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