A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 1
... solid body . If the vessel be now brought to rest , the motion of the fluid continues for some time , but gradually subsides , and at length ceases altogether ; and it is found that L. 1 CHAPTER THE EQUATIONS OF MOTION.
... solid body . If the vessel be now brought to rest , the motion of the fluid continues for some time , but gradually subsides , and at length ceases altogether ; and it is found that L. 1 CHAPTER THE EQUATIONS OF MOTION.
Page 19
... rest under the action of forces of the kind here supposed ; for then we have , initially , or udx + vdy + wdz = 0 , $ = const . Again , if the motion be so slow that the squares and products of u , v , w and their first differential ...
... rest under the action of forces of the kind here supposed ; for then we have , initially , or udx + vdy + wdz = 0 , $ = const . Again , if the motion be so slow that the squares and products of u , v , w and their first differential ...
Page 21
... rest by the application of a properly chosen system of impulsive pressures . This is evident from equations ( 21 ) Art . 15 , which shew , moreover , that $ == ♡ Р + const .; so that C - pp gives the requisite system . In σ = the same ...
... rest by the application of a properly chosen system of impulsive pressures . This is evident from equations ( 21 ) Art . 15 , which shew , moreover , that $ == ♡ Р + const .; so that C - pp gives the requisite system . In σ = the same ...
Page 30
... rest under the action of the forces X = Ax + By , Y = Bx + Cy , Z = 0 , the axis of z being that of the cylinder . Let us assume u = - · wy , v = wx , w = 0 , where w is a function of t only . These values satisfy the equation of ...
... rest under the action of the forces X = Ax + By , Y = Bx + Cy , Z = 0 , the axis of z being that of the cylinder . Let us assume u = - · wy , v = wx , w = 0 , where w is a function of t only . These values satisfy the equation of ...
Page 37
... rest of this chapter is devoted to the study of irrota- tional motion , as defined by the equations = 0 , n = 0 , C = 0 ....... ( 8 ) . The existence and the properties of the velocity - potential in the various cases that may arise ...
... rest of this chapter is devoted to the study of irrota- tional motion , as defined by the equations = 0 , n = 0 , C = 0 ....... ( 8 ) . The existence and the properties of the velocity - potential in the various cases that may arise ...
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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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