A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 3
... Hence if we form the equation of motion of the tetrahedron parallel to PA we have P1 . lA = pl . △ , where we have omitted the terms which express the rate of change of momentum , and the component of the external im- pressed forces ...
... Hence if we form the equation of motion of the tetrahedron parallel to PA we have P1 . lA = pl . △ , where we have omitted the terms which express the rate of change of momentum , and the component of the external im- pressed forces ...
Page 7
... Hence if in any of our investigations we be led to negative values of p , the state of motion given by the formulæ is an impossible one . At the moment when , according to the form- ulæ , p would change from positive through zero to ...
... Hence if in any of our investigations we be led to negative values of p , the state of motion given by the formulæ is an impossible one . At the moment when , according to the form- ulæ , p would change from positive through zero to ...
Page 11
... Hence , or Similarly , pdx dydz ( u ' — u ) = pdx dy dz X ' - 1 do u'u X'- P dx . v'v = Y ' w ' - w = Z ' - - ρ 1 do p dy ' 1 do p dz da - dx dx dy dz , . ( 19 ) . These equations might also have been deduced from ( 2 12-15 . ] . 11 ...
... Hence , or Similarly , pdx dydz ( u ' — u ) = pdx dy dz X ' - 1 do u'u X'- P dx . v'v = Y ' w ' - w = Z ' - - ρ 1 do p dy ' 1 do p dz da - dx dx dy dz , . ( 19 ) . These equations might also have been deduced from ( 2 12-15 . ] . 11 ...
Page 12
... Hence , in applying ( 19 ) to the case of a gas we must put = 0 , whence u ' - u = X ' , v ' - v = Y ' , w ' - w = Z ' . .... . ( 20 ) . In a liquid , on the other hand , an instantaneous change of motion can be produced by the action ...
... Hence , in applying ( 19 ) to the case of a gas we must put = 0 , whence u ' - u = X ' , v ' - v = Y ' , w ' - w = Z ' . .... . ( 20 ) . In a liquid , on the other hand , an instantaneous change of motion can be produced by the action ...
Page 14
... Hence , since the mass of the element is unchanged , we have d ( x , y , z ) Р = Po d ( a , b , c ) ( 23 ) , where Po is the initial density at ( a , b , c ) . In the case of an incompressible fluid p = P。, so that ( 23 ) becomes d ( x ...
... Hence , since the mass of the element is unchanged , we have d ( x , y , z ) Р = Po d ( a , b , c ) ( 23 ) , where Po is the initial density at ( a , b , c ) . In the case of an incompressible fluid p = P。, so that ( 23 ) becomes d ( x ...
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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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