A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 7
... side to the other , we have dF dF dF dt dF + U1 dx dF +21 dy dF and dt + Uq dx + V2 dy dF + w1 dz dF + wz dz = = 0 , 0 , where the suffixes are used to distinguish the two sides 8-10 . ] 7 SURFACE CONDITIONS .
... side to the other , we have dF dF dF dt dF + U1 dx dF +21 dy dF and dt + Uq dx + V2 dy dF + w1 dz dF + wz dz = = 0 , 0 , where the suffixes are used to distinguish the two sides 8-10 . ] 7 SURFACE CONDITIONS .
Page 8
... sides . 11. The equation ( 11 ) expresses the condition that if the motion be continuous the particles which at any instant lie in the bounding surface lie in it always . For ( 11 ) expresses that no fluid crosses the surface F = 0 ...
... sides . 11. The equation ( 11 ) expresses the condition that if the motion be continuous the particles which at any instant lie in the bounding surface lie in it always . For ( 11 ) expresses that no fluid crosses the surface F = 0 ...
Page 25
... sides towards the orifice . Its motion is not , therefore , throughout the area of the orifice , everywhere perpendicular to this area ; but becomes more and more oblique as we pass from the centre of the orifice to the sides . Again ...
... sides towards the orifice . Its motion is not , therefore , throughout the area of the orifice , everywhere perpendicular to this area ; but becomes more and more oblique as we pass from the centre of the orifice to the sides . Again ...
Page 27
... side of ( 16 ) is therefore too small , and the ratio S ' : S is really greater than 1 . The above theory is taken from a paper by Mr G. O. Hanlon , in the 3rd volume of the Proceedings of the London Mathematical Society , and from a ...
... side of ( 16 ) is therefore too small , and the ratio S ' : S is really greater than 1 . The above theory is taken from a paper by Mr G. O. Hanlon , in the 3rd volume of the Proceedings of the London Mathematical Society , and from a ...
Page 33
... side of the equations ( 2 ) , is a motion such that every point on the quadric aX2 + bY2 + cZ2 + 2ƒYZ + 2gZX + 2hXY = const . . ( 3 ) , ...... is moving in the direction of the normal to the surface . If we refer this quadric to its ...
... side of the equations ( 2 ) , is a motion such that every point on the quadric aX2 + bY2 + cZ2 + 2ƒYZ + 2gZX + 2hXY = const . . ( 3 ) , ...... is moving in the direction of the normal to the surface . If we refer this quadric to its ...
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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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