A Treatise on the Mathematical Theory of the Motion of FluidsThe University Press, 1879 - 258 pagina's |
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Pagina 69
... circle , and if r , ✪ be polar co - ordinates referred to the centre P of this circle as origin , the equation ( 8 ) may be written or 2π do . rd0 = 0 , 0 d dr dr S 2π фа0 = 0 . 0 1 Hence the value of the integral føde , i.e. the mean ...
... circle , and if r , ✪ be polar co - ordinates referred to the centre P of this circle as origin , the equation ( 8 ) may be written or 2π do . rd0 = 0 , 0 d dr dr S 2π фа0 = 0 . 0 1 Hence the value of the integral føde , i.e. the mean ...
Pagina 70
... circle embraces the same internal boundary , and lies itself wholly in the fluid . If the region be unlimited externally , and if the circle embrace the whole of the internal boundaries , and if further the velocity be everywhere zero ...
... circle embraces the same internal boundary , and lies itself wholly in the fluid . If the region be unlimited externally , and if the circle embrace the whole of the internal boundaries , and if further the velocity be everywhere zero ...
Pagina 71
Sir Horace Lamb. For if we introduce a circle of great radius r as the external boundary of the portion of the plane xy considered , we find that the corresponding part of the integral on the right - hand side of ( 10 ) tends , as r ...
Sir Horace Lamb. For if we introduce a circle of great radius r as the external boundary of the portion of the plane xy considered , we find that the corresponding part of the integral on the right - hand side of ( 10 ) tends , as r ...
Pagina 76
... circle having the origin as centre is dz = fido = 2πi . In the analytical theory above referred to , the logarithm of a complex quantity z is defined by the equation rz dz log z = 2 .... ( 20 ) . Hence log z is a many - valued function ...
... circle having the origin as centre is dz = fido = 2πi . In the analytical theory above referred to , the logarithm of a complex quantity z is defined by the equation rz dz log z = 2 .... ( 20 ) . Hence log z is a many - valued function ...
Pagina 78
... circle of to the point P ( x , y ) of the plane of z . Fig . 5 . Z е 3 ພ radius unity about the origin , starting from the point ( 1 , 0 ) ; then , since log 10 , P ' will move along the axis of , and will describe a length 27 of that ...
... circle of to the point P ( x , y ) of the plane of z . Fig . 5 . Z е 3 ພ radius unity about the origin , starting from the point ( 1 , 0 ) ; then , since log 10 , P ' will move along the axis of , and will describe a length 27 of that ...
Overige edities - Alles bekijken
A Treatise on the Mathematical Theory of the Motion of Fluids Sir Horace Lamb Volledige weergave - 1879 |
A Treatise on the Mathematical Theory of the Motion of Fluids Sir Horace Lamb Volledige weergave - 1879 |
A Treatise on the Mathematical Theory of the Motion of Fluids Sir Horace Lamb Volledige weergave - 1879 |
Veelvoorkomende woorden en zinsdelen
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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