A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 4
... centre at ( x , y , z ) , and its edges dx , dy , dz parallel to the co- ordinate axes . The rate at which the x - component of the momen- ди tum of this element is increasing is pdxdydz ; and this must Ət be equal to the x - component ...
... centre at ( x , y , z ) , and its edges dx , dy , dz parallel to the co- ordinate axes . The rate at which the x - component of the momen- ди tum of this element is increasing is pdxdydz ; and this must Ət be equal to the x - component ...
Page 9
... centre at ( x , y , z ) . This is expressed by dQ dt dx dy dz ....... .. ( 14 ) . Now the amount of Q which enters per unit time the specified region across the yz - face nearest the origin is ( Qu — ( Qu- d . Qu da ) dy dz , and dx the ...
... centre at ( x , y , z ) . This is expressed by dQ dt dx dy dz ....... .. ( 14 ) . Now the amount of Q which enters per unit time the specified region across the yz - face nearest the origin is ( Qu — ( Qu- d . Qu da ) dy dz , and dx the ...
Page 25
... centre of the orifice to the sides . Again , the converging motion of the elementary streams must make the pressure at the orifice somewhat greater in the interior of the jet than at its surface , where it is equal to the atmospheric ...
... centre of the orifice to the sides . Again , the converging motion of the elementary streams must make the pressure at the orifice somewhat greater in the interior of the jet than at its surface , where it is equal to the atmospheric ...
Page 26
... centre of inertia of the orifice . It is this force which produces the momentum with which the fluid leaves the vessel . The mass of fluid which in unit time 26 INTEGRATION OF THE EQUATIONS IN SPECIAL CASES . [ CHAP . II .
... centre of inertia of the orifice . It is this force which produces the momentum with which the fluid leaves the vessel . The mass of fluid which in unit time 26 INTEGRATION OF THE EQUATIONS IN SPECIAL CASES . [ CHAP . II .
Page 33
... centre may be conceived as made up of three parts . The first part , whose components are u , v , w , is a motion of translation of the element as a whole , The second part , expressed by the second , third , and fourth terms on the ...
... centre may be conceived as made up of three parts . The first part , whose components are u , v , w , is a motion of translation of the element as a whole , The second part , expressed by the second , third , and fourth terms on the ...
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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 constant corresponding Crown 8vo curves const cyclic Demy 8vo denote direction dt dt dx dx dx dy dz dy dy Edited element equation of continuity Fellow finite fluid forces formulæ given Green's Theorem Hence impulse infinitely small infinity integral internal boundary irrotational irrotational motion J. E. SANDYS liquid LL.D mass moving Notes obtain origin P. G. TAIT P₁ parallel particle plane xy portion pressure Professor quantities radius RENDEL HARRIS satisfied shews simply-connected solid sphere St John's College stream-lines surface theorem Thomson Trinity College University of Cambridge University Press Warehouse velocity-potential vertical vortex waves zero аф
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