A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 12
... limits 0 and 7 , putting X ' = [ ' " Xdt , & c . , ≈ = - = [ pdt , and then making ☛ vanish . T In a gas an infinite pressure would involve an infinite density ; whereas no change of density can occur during the infinitely short time ...
... limits 0 and 7 , putting X ' = [ ' " Xdt , & c . , ≈ = - = [ pdt , and then making ☛ vanish . T In a gas an infinite pressure would involve an infinite density ; whereas no change of density can occur during the infinitely short time ...
Page 15
Sir Horace Lamb. Let us integrate these equations with respect to t between the limits 0 and t . We remark that d2x dx 0 I. dt dx dxt = - dt2 da dt da 0 dx dx = Ио dt da ... limit of integration in ( 25 ) . We 17-19 . ] 15 WEBER'S EQUATIONS .
Sir Horace Lamb. Let us integrate these equations with respect to t between the limits 0 and t . We remark that d2x dx 0 I. dt dx dxt = - dt2 da dt da 0 dx dx = Ио dt da ... limit of integration in ( 25 ) . We 17-19 . ] 15 WEBER'S EQUATIONS .
Page 16
Sir Horace Lamb. upper limit of integration in ( 25 ) . We find x = - V'- ' @ P where is the impulsive pressure and V ' the potential of the external impulsive forces at the point ( a , b , c ) . we have , by ( 26 ) , dr dt - Ио = da dV ...
Sir Horace Lamb. upper limit of integration in ( 25 ) . We find x = - V'- ' @ P where is the impulsive pressure and V ' the potential of the external impulsive forces at the point ( a , b , c ) . we have , by ( 26 ) , dr dt - Ио = da dV ...
Page 24
... limit which the velocity cannot exceed if the motion be continuous . For instance , let us suppose that we have a liquid flowing from a reservoir where the motion is sensibly zero , and the pressure equal to P , and that we may neglect ...
... limit which the velocity cannot exceed if the motion be continuous . For instance , let us suppose that we have a liquid flowing from a reservoir where the motion is sensibly zero , and the pressure equal to P , and that we may neglect ...
Page 38
... limit in ( 9 ) , simply adds an arbitrary constant to the value of p , viz . the flow from B to A. The original definition of 4 in Art . 22 , and its physical interpretation in Art . 26 , leave the function indeterminate to the extent ...
... limit in ( 9 ) , simply adds an arbitrary constant to the value of p , viz . the flow from B to A. The original definition of 4 in Art . 22 , and its physical interpretation in Art . 26 , leave the function indeterminate to the extent ...
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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 formulę 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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