A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 13
... differential element of volume dxdydz , we find by the same reasoning as in Art . 6 , d'x dt2 d3y dt2 d2z dt = = = X Y Z - 1 1 dp ρ p dx 1 dp p dy 1 dp P dz These equations contain differential coefficients with respect to x , y , z ...
... differential element of volume dxdydz , we find by the same reasoning as in Art . 6 , d'x dt2 d3y dt2 d2z dt = = = X Y Z - 1 1 dp ρ p dx 1 dp p dy 1 dp P dz These equations contain differential coefficients with respect to x , y , z ...
Page 14
... differential coefficients with respect to x , y , z of a single function which we denote by V ( so that Vis the potential energy , due to those forces , of unit mass placed in the position ( x , y , z ) ) , the equations ( 22 ) may be ...
... differential coefficients with respect to x , y , z of a single function which we denote by V ( so that Vis the potential energy , due to those forces , of unit mass placed in the position ( x , y , z ) ) , the equations ( 22 ) may be ...
Page 15
... differential equa- tions to be satisfied by the five unknown quantities x , y , z , P , X ; p being supposed already eliminated by means of one of the rela- tions of Art . 7 . In the case of a liquid , p occurs in ( 27 ) only , so that ...
... differential equa- tions to be satisfied by the five unknown quantities x , y , z , P , X ; p being supposed already eliminated by means of one of the rela- tions of Art . 7 . In the case of a liquid , p occurs in ( 27 ) only , so that ...
Page 16
... differential coefficients . In Weber's transformation the latter are replaced by a system of equations of the first order , and of the second degree . The Eulerian equation of continuity is also much simpler than the Lagrangian ...
... differential coefficients . In Weber's transformation the latter are replaced by a system of equations of the first order , and of the second degree . The Eulerian equation of continuity is also much simpler than the Lagrangian ...
Page 18
... differential coefficients of a function 4 , so that u = аф dx ' v = аф dy ' do w = dz . ( 2 ) . Such a function is called a ' velocity - potential , ' from its analogy to the potential function which occurs in the theories of ...
... differential coefficients of a function 4 , so that u = аф dx ' v = аф dy ' do w = dz . ( 2 ) . Such a function is called a ' velocity - potential , ' from its analogy to the potential function which occurs in the theories of ...
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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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