A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page viii
... formulæ for the velocity potential and the stream - function 84 Motion of a circular cylinder in a liquid . 38 80 88 . Motion of translation of a solid through a liquid . 87 Examples . 89 . Motion of rotation of a solid in a liquid 91 ...
... formulæ for the velocity potential and the stream - function 84 Motion of a circular cylinder in a liquid . 38 80 88 . Motion of translation of a solid through a liquid . 87 Examples . 89 . Motion of rotation of a solid in a liquid 91 ...
Page x
... Formulæ of transformation 216 178 . Relations between the stresses across different planes . Stresses in terms of rates of strain 218 Coefficient of viscosity . 179 . Dissipation - function 220 180 , 181 . Equations of motion 221 223 ...
... Formulæ of transformation 216 178 . Relations between the stresses across different planes . Stresses in terms of rates of strain 218 Coefficient of viscosity . 179 . Dissipation - function 220 180 , 181 . Equations of motion 221 223 ...
Page 7
... formulæ is an impossible one . At the moment when , according to the form- ulæ , p would change from positive through zero to negative , either the fluid parts asunder , or a surface of discontinuity is formed , so that the conditions ...
... formulæ is an impossible one . At the moment when , according to the form- ulæ , p would change from positive through zero to negative , either the fluid parts asunder , or a surface of discontinuity is formed , so that the conditions ...
Page 8
... formulæ u = ± x , v = c , w = 0 , the upper sign in u being taken for points receding from the fixed boundary x = 0 , the lower for points approaching it . portion of matter as it moves along . In another 8 [ CHAP . I. THE EQUATIONS OF ...
... formulæ u = ± x , v = c , w = 0 , the upper sign in u being taken for points receding from the fixed boundary x = 0 , the lower for points approaching it . portion of matter as it moves along . In another 8 [ CHAP . I. THE EQUATIONS OF ...
Page 33
... formulæ ( 4 ) express that the length of every line in the element parallel to X ' is being elongated at the rate ( positive or negative ) a ' , whilst lines parallel to Y ′ and Z ′ are being similarly elongated at the rates b ' and c ...
... formulæ ( 4 ) express that the length of every line in the element parallel to X ' is being elongated at the rate ( positive or negative ) a ' , whilst lines parallel to Y ′ and Z ′ are being similarly elongated at the rates b ' and c ...
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Common terms and phrases
angle angular velocity Ave Maria Lane axes axis C. J. CLAY Cambridge University Press centre Christ's College circle circuit CLAY & SONS co-ordinates component constant corresponding Crown 8vo cyclic Demy 8vo denote direction dT dT dx dx dx dy dz dy dy dydz Edited element equation of continuity equations of motion Fellow finite fluid forces formula formulæ given Green's Theorem Hence independent circuits infinitely small infinity integral internal boundary irrotational motion liquid LL.D mass moving Notes obtain origin P. G. TAIT parallel particle perpendicular plane xy portion Professor quantities radius RENDEL HARRIS satisfied shews side simply-connected solid sphere St John's College stream-lines surface theorem theory Thomson Trans Trinity College University of Cambridge University Press Warehouse velocity-potential vortex waves zero аф
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