A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page viii
... of a solid of revolution in a particular case . Stability of a body moving parallel to an axis of symmetry Constraint necessary to produce any specified motion 124 126 129 130 133 134 135 ART . 120 , 121 . 122 , 123 . viii CONTENTS .
... of a solid of revolution in a particular case . Stability of a body moving parallel to an axis of symmetry Constraint necessary to produce any specified motion 124 126 129 130 133 134 135 ART . 120 , 121 . 122 , 123 . viii CONTENTS .
Page 3
... parallel to PA we have P1 . lA = pl . △ , where we have omitted the terms which express the rate of change of momentum , and the component of the external im- pressed forces , because they are ultimately proportional to the mass of the ...
... parallel to PA we have P1 . lA = pl . △ , where we have omitted the terms which express the rate of change of momentum , and the component of the external im- pressed forces , because they are ultimately proportional to the mass of the ...
Page 4
... parallel to the co- ordinate axes . The rate at which the x - component of the momen- tum of this element is increasing is pdxdydz ди t ; and this must be equal to the x - component of the forces acting on the element . Of these the ...
... parallel to the co- ordinate axes . The rate at which the x - component of the momen- tum of this element is increasing is pdxdydz ди t ; and this must be equal to the x - component of the forces acting on the element . Of these the ...
Page 8
... parallel and infinitely close to F = 0 , and suppose it to move with the particles of which it is composed , the stratum of fluid which is included between this and F = 0 , and which in virtue of the continuity of the motion remains ...
... parallel and infinitely close to F = 0 , and suppose it to move with the particles of which it is composed , the stratum of fluid which is included between this and F = 0 , and which in virtue of the continuity of the motion remains ...
Page 9
... parallel to x per unit mass . The momentum con- tained in the space dxdy dz is affected not only by the passage of matter carrying its momentum with it across the boundary , but also by the forces acting on the included matter , viz ...
... parallel to x per unit mass . The momentum con- tained in the space dxdy dz is affected not only by the passage of matter carrying its momentum with it across the boundary , but also by the forces acting on the included matter , viz ...
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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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