A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 1
... exist in fluids in motion . Let us suppose for instance that a vessel in the form of a circular cylinder , containing water ( or other liquid ) , is made to rotate about its axis , which is vertical . If the motion of the vessel be ...
... exist in fluids in motion . Let us suppose for instance that a vessel in the form of a circular cylinder , containing water ( or other liquid ) , is made to rotate about its axis , which is vertical . If the motion of the vessel be ...
Page 17
... exist varies in conse- quence of the motion which we have to investigate . In the other method , on the contrary , the range of values of the independent variables a , b , c is given once for all by the initial conditions . The ...
... exist varies in conse- quence of the motion which we have to investigate . In the other method , on the contrary , the range of values of the independent variables a , b , c is given once for all by the initial conditions . The ...
Page 18
... exist , at any one instant , for any finite portion of a perfect fluid in motion under the action of forces which have ... exists be taken as the origin of time ; we have then uda + v.db + w , dc = do , throughout the portion of the mass ...
... exist , at any one instant , for any finite portion of a perfect fluid in motion under the action of forces which have ... exists be taken as the origin of time ; we have then uda + v.db + w , dc = do , throughout the portion of the mass ...
Page 19
... exists moves about and carries this property with it , but the portion of space which it originally occupied may , in the course of the motion , come to be occupied by matter which did not originally possess this property , and which ...
... exists moves about and carries this property with it , but the portion of space which it originally occupied may , in the course of the motion , come to be occupied by matter which did not originally possess this property , and which ...
Page 20
... exists . 25. Under the circumstances stated in Art . 23 , the equations of Art . 6 are at once integrable throughout that portion of the mass for which a velocity - potential exists . For , in virtue of the rela- dv dw dw du du dv ...
... exists . 25. Under the circumstances stated in Art . 23 , the equations of Art . 6 are at once integrable throughout that portion of the mass for which a velocity - potential exists . For , in virtue of the rela- dv dw dw du du dv ...
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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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