A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 12
... whole history of every particle of the fluid . The velocities parallel to the axes of co - ordinates of * It will appear in Chapter III . that ( save as to additive constants ) there is only one value of which does this . dx dy dz dt ...
... whole history of every particle of the fluid . The velocities parallel to the axes of co - ordinates of * It will appear in Chapter III . that ( save as to additive constants ) there is only one value of which does this . dx dy dz dt ...
Page 23
... whole , so that 2 12 12 pqo + pqo ( ¿ q2 + V ) = p'q'o ' + pq'o ' ( ¿ q ′′ 2 + V ' ) . Dividing by pqo ( = pq'o ' ) , we have Ρ 2 + £ q2 + V = p ' / 2 + 1 q2 + V ' , P ρ or , using C in the same sense as before 27-29 . ] 23 STREAM - LINES .
... whole , so that 2 12 12 pqo + pqo ( ¿ q2 + V ) = p'q'o ' + pq'o ' ( ¿ q ′′ 2 + V ' ) . Dividing by pqo ( = pq'o ' ) , we have Ρ 2 + £ q2 + V = p ' / 2 + 1 q2 + V ' , P ρ or , using C in the same sense as before 27-29 . ] 23 STREAM - LINES .
Page 30
... whole about the axis of z with uniformly increasing angular velocity , except in the particular case when BB ' . To find p , we substitute the value of and integrate ; thus we get do dt · ? = { w2 ( x2 + y2 ) + + ( Ax2 + 2ßxy + Cy3 ) + ...
... whole about the axis of z with uniformly increasing angular velocity , except in the particular case when BB ' . To find p , we substitute the value of and integrate ; thus we get do dt · ? = { w2 ( x2 + y2 ) + + ( Ax2 + 2ßxy + Cy3 ) + ...
Page 33
... whole , The second part , expressed by the second , third , and fourth terms on the right - hand side of the equations ( 2 ) , is a motion such that every point on the quadric aX2 + bY2 + cZ3 + 2ƒYZ + 2gZX + 2hXY = const . ( 3 ) ...
... whole , The second part , expressed by the second , third , and fourth terms on the right - hand side of the equations ( 2 ) , is a motion such that every point on the quadric aX2 + bY2 + cZ3 + 2ƒYZ + 2gZX + 2hXY = const . ( 3 ) ...
Page 39
... whole boundary of the region . Equations ( 10 ) and ( 11 ) , expressing the same fact , must be mathe- matically equivalent ; see Art . 64 . The stream - lines drawn through the various points of an infinitesimal circuit constitute a ...
... whole boundary of the region . Equations ( 10 ) and ( 11 ) , expressing the same fact , must be mathe- matically equivalent ; see Art . 64 . The stream - lines drawn through the various points of an infinitesimal circuit constitute a ...
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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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