A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page viii
... 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 .
... 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 4
... moving particle . This we shall denote by OF It a at the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the ...
... moving particle . This we shall denote by OF It a at the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the ...
Page 5
... moving element of fluid , we have , on account of the constancy of mass , or a.pv = 0 Ət ap √ + P at at av 0 ( 6 ) . Now the rate of increase of volume of a moving region is evid- ently expressed by the surface - integral of the normal ...
... moving element of fluid , we have , on account of the constancy of mass , or a.pv = 0 Ət ap √ + P at at av 0 ( 6 ) . Now the rate of increase of volume of a moving region is evid- ently expressed by the surface - integral of the normal ...
Page 8
... moving solid . The truth of ( 13 ) , of which ( 12 ) is a particular case , is other- wise obvious from the consideration that the velocity normal to the surface must be , in each of the cases mentioned , the same on both sides . 11 ...
... moving solid . The truth of ( 13 ) , of which ( 12 ) is a particular case , is other- wise obvious from the consideration that the velocity normal to the surface must be , in each of the cases mentioned , the same on both sides . 11 ...
Page 17
... moving surface , the Lagrangian method possesses certain theoreti- cal advantages . In the Eulerian method the functions u , v , w . have no existence beyond this surface , and hence the range of values of x , y , z for which these ...
... moving surface , the Lagrangian method possesses certain theoreti- cal advantages . In the Eulerian method the functions u , v , w . have no existence beyond this surface , and hence the range of values of x , y , z for which these ...
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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 constant corresponding Crown 8vo curves const cyclic Demy 8vo denote direction dt dt dx dx dx dy dz dy dy Edited element equation of continuity Fellow finite fluid forces formulæ given Green's Theorem Hence impulse infinitely small infinity integral internal boundary irrotational irrotational motion J. E. SANDYS liquid LL.D mass moving Notes obtain origin P. G. TAIT P₁ parallel particle plane xy portion pressure Professor quantities radius RENDEL HARRIS satisfied shews simply-connected solid sphere St John's College stream-lines surface theorem Thomson Trinity College University of Cambridge University Press Warehouse velocity-potential vertical vortex waves zero аф
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