A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 3
... positive when pressures , negative when tensions . Ordinary fluids are , however , incapable of supporting more than an exceedingly slight degree of tension , so that p is nearly always positive . + Principes généraux du mouvement des ...
... positive when pressures , negative when tensions . Ordinary fluids are , however , incapable of supporting more than an exceedingly slight degree of tension , so that p is nearly always positive . + Principes généraux du mouvement des ...
Page 4
... positive . The pressures on the remaining faces are perpendicular to x . We have then ди pdx dy dz = pdx dy dz X - P dxdydz . dp θε dx Ju Substituting the value of Ət from ( 1 ) 4 [ CHAP . I. THE EQUATIONS OF MOTION .
... positive . The pressures on the remaining faces are perpendicular to x . We have then ди pdx dy dz = pdx dy dz X - P dxdydz . dp θε dx Ju Substituting the value of Ət from ( 1 ) 4 [ CHAP . I. THE EQUATIONS OF MOTION .
Page 6
... , 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 MOTION .
... , 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 MOTION .
Page 7
... positive through zero to negative , either the fluid parts asunder , or a surface of discontinuity is formed , so that the conditions of the problem are entirely changed . See Art . 94 . The quantity p is finite and positive , but not ...
... positive through zero to negative , either the fluid parts asunder , or a surface of discontinuity is formed , so that the conditions of the problem are entirely changed . See Art . 94 . The quantity p is finite and positive , but not ...
Page 25
... positive direction downwards , so that V = — gz . If we suppose the area of the upper surface large compared with that of the orifice , the velocity at the former may be neglected . Hence , determining the constant in ( 10 ) so that p ...
... positive direction downwards , so that V = — gz . If we suppose the area of the upper surface large compared with that of the orifice , the velocity at the former may be neglected . Hence , determining the constant in ( 10 ) so that p ...
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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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