A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 2
... constant . We infer , moreover , that these tangential stresses are not called into play so long as the fluid moves as a solid body , but only whilst a change of shape of some portion of the mass is going on , and that their tendency is ...
... constant . We infer , moreover , that these tangential stresses are not called into play so long as the fluid moves as a solid body , but only whilst a change of shape of some portion of the mass is going on , and that their tendency is ...
Page 5
... constant ...... ...... . ( 5 ) . 8. The remaining equation is a kinematical relation between u , v , w , p obtained as follows . If V denote the volume of a moving element of fluid , we have , on account of the constancy of mass , a.pv ...
... constant ...... ...... . ( 5 ) . 8. The remaining equation is a kinematical relation between u , v , w , p obtained as follows . If V denote the volume of a moving element of fluid , we have , on account of the constancy of mass , a.pv ...
Page 12
... axes of co - ordinates of * It will appear in Chapter III . that ( save as to additive constants ) there is only one value of which does this . dx dy dz dt ' the particle ( a , 12 [ CHAP . I. THE EQUATIONS OF MOTION .
... axes of co - ordinates of * It will appear in Chapter III . that ( save as to additive constants ) there is only one value of which does this . dx dy dz dt ' the particle ( a , 12 [ CHAP . I. THE EQUATIONS OF MOTION .
Page 18
... constant or a function of the pressure only , a velocity - potential exists for the same portion of the fluid at all subsequent instants . In the equations of Art . 18 , let the instant at which the velocity - potential , exists be ...
... constant or a function of the pressure only , a velocity - potential exists for the same portion of the fluid at all subsequent instants . In the equations of Art . 18 , let the instant at which the velocity - potential , exists be ...
Page 21
... constant in these expressions shews , what is otherwise evident , that a pressure uniform throughout a liquid mass produces no effect on its motion . In the case of a gas , is the potential of the external im- pulsive forces by which ...
... constant in these expressions shews , what is otherwise evident , that a pressure uniform throughout a liquid mass produces no effect on its motion . In the case of a gas , is the potential of the external im- pulsive forces by which ...
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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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