A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 28
... angular velocity w about the axis of z supposed drawn vertically upwards . also By hypothesis , u == wy , v = wx , w = 0 ; X = 0 , Y = 0 , Z = -g . The equation of continuity is identically satisfied , and the dynamical equations of ...
... angular velocity w about the axis of z supposed drawn vertically upwards . also By hypothesis , u == wy , v = wx , w = 0 ; X = 0 , Y = 0 , Z = -g . The equation of continuity is identically satisfied , and the dynamical equations of ...
Page 29
... angular velocity w to be uniform , let us suppose it to be a function of the distance r from that axis , and let us inquire what form must be assigned to this function in order that a velocity - potential may exist for the motion . We ...
... angular velocity w to be uniform , let us suppose it to be a function of the distance r from that axis , and let us inquire what form must be assigned to this function in order that a velocity - potential may exist for the motion . We ...
Page 30
... angular velocity , except in the particular case when BB ' . To find p , we substitute the value of and integrate ; thus we get P = ρ dw in ( 20 ) dt · { w2 ( x2 + y2 ) + † ( Ax2 + 2ẞxy + Cy3 ) + const . , where 28 B + B ' . 37. Example ...
... angular velocity , except in the particular case when BB ' . To find p , we substitute the value of and integrate ; thus we get P = ρ dw in ( 20 ) dt · { w2 ( x2 + y2 ) + † ( Ax2 + 2ẞxy + Cy3 ) + const . , where 28 B + B ' . 37. Example ...
Page 31
... angular velocity dt which varies inversely as the square of the distance from the axis , and increases uniformly with the time . CHAPTER III . IRROTATIONAL MOTION . 38. THE present chapter 35-37 . ] 31 ROTATING FLUID .
... angular velocity dt which varies inversely as the square of the distance from the axis , and increases uniformly with the time . CHAPTER III . IRROTATIONAL MOTION . 38. THE present chapter 35-37 . ] 31 ROTATING FLUID .
Page 33
... angular velocities of the rotation being § , n , . It can be shewn that the above resolution of the motion is unique . If we assume that the motion relative to the point ( x , y , z ) can be made up of a distortion and a rotation in ...
... angular velocities of the rotation being § , n , . It can be shewn that the above resolution of the motion is unique . If we assume that the motion relative to the point ( x , y , z ) can be made up of a distortion and a rotation in ...
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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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