A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 10
... contained within the space dx dydz is due to the flow of matter carrying its energy with it , and to the work done on the con- tained matter by the pressure of the surrounding fluid . The total rate at which this pressure works is - ( d ...
... contained within the space dx dydz is due to the flow of matter carrying its energy with it , and to the work done on the con- tained matter by the pressure of the surrounding fluid . The total rate at which this pressure works is - ( d ...
Page 13
... contain differential coefficients with respect to x , y , z , whereas our independent variables are a , b , c , t . To eliminate these differential coefficients , we multiply the above dx dy dz equations by da'da da respectively , and ...
... contain differential coefficients with respect to x , y , z , whereas our independent variables are a , b , c , t . To eliminate these differential coefficients , we multiply the above dx dy dz equations by da'da da respectively , and ...
Page 16
... contain products of 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 ...
... contain products of 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 ...
Page 20
... contain t . In some cases , for example , when the motion is wholly periodic , we can assert that the latter part is zero , and therefore , that a velocity - potential exists . 25. Under the circumstances stated in Art . 23 , the ...
... contain t . In some cases , for example , when the motion is wholly periodic , we can assert that the latter part is zero , and therefore , that a velocity - potential exists . 25. Under the circumstances stated in Art . 23 , the ...
Page 43
... contained within it . This is however , as we have seen , inconsistent with the other conditions which the stream - lines must conform to . Hence , as before , there can be no motion , and & is constant . This theorem may be otherwise ...
... contained within it . This is however , as we have seen , inconsistent with the other conditions which the stream - lines must conform to . Hence , as before , there can be no motion , and & is constant . This theorem may be otherwise ...
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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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