A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 2
... mass is going on , and that their tendency is to oppose this change of shape . 3. It is usual , however , in the first instance , to neglect the tangential stresses altogether . Their effect is in many practical cases small , but ...
... mass is going on , and that their tendency is to oppose this change of shape . 3. It is usual , however , in the first instance , to neglect the tangential stresses altogether . Their effect is in many practical cases small , but ...
Page 3
... mass of the tetrahedron , and therefore of the third order of small quantities , whilst the terms retained in the equation of motion are of the second . We have then , ultimately , p = p1 , and similarly P = P , P. , which proves the ...
... mass of the tetrahedron , and therefore of the third order of small quantities , whilst the terms retained in the equation of motion are of the second . We have then , ultimately , p = p1 , and similarly P = P , P. , which proves the ...
Page 4
... mass , at the point ( x , y , z ) at the time t . Let us take a rectangular element having its centre at ( x , y , z ) , and its edges dx , dy , dz parallel to the co- ordinate axes . The rate at which the x - component of the momen ...
... mass , at the point ( x , y , z ) at the time t . Let us take a rectangular element having its centre at ( x , y , z ) , and its edges dx , dy , dz parallel to the co- ordinate axes . The rate at which the x - component of the momen ...
Page 5
... mass , a.pv Ət = 0 ap √ + P at av = 0 ..... . ( 6 ) . or at Now the rate of increase of volume of a moving region is evid- ently expressed by the surface - integral of the normal velocity outwards , taken all over the boundary . If the ...
... mass , a.pv Ət = 0 ap √ + P at av = 0 ..... . ( 6 ) . or at Now the rate of increase of volume of a moving region is evid- ently expressed by the surface - integral of the normal velocity outwards , taken all over the boundary . If the ...
Page 6
... mass , a certain condition , given in Art . 10 , must be satisfied at such a surface . The quantity p is necessarily continuous , and finite . It is also essentially positive , at all events in the case of 6 [ CHAP . I. THE EQUATIONS OF ...
... mass , a certain condition , given in Art . 10 , must be satisfied at such a surface . The quantity p is necessarily continuous , and finite . It is also essentially positive , at all events in the case of 6 [ CHAP . I. THE EQUATIONS 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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