A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page ix
... Determination of motion in terms of expansion and rotation Interpretation . Electromagnetic analogy . 132 . Vortex - Sheet . " 133 . Velocity - Potential due to a vortex . 134 . Dynamical theorems 135-137 . Kinetic Energy 138 , 139 ...
... Determination of motion in terms of expansion and rotation Interpretation . Electromagnetic analogy . 132 . Vortex - Sheet . " 133 . Velocity - Potential due to a vortex . 134 . Dynamical theorems 135-137 . Kinetic Energy 138 , 139 ...
Page 3
... determining the motion of a fluid mass , acted on by given forces and subject to given conditions , may be viewed ... determine the history of each individual particle . The equations obtained on these two plans are conveniently ...
... determining the motion of a fluid mass , acted on by given forces and subject to given conditions , may be viewed ... determine the history of each individual particle . The equations obtained on these two plans are conveniently ...
Page 12
... determine a value of satisfying this equation and the proper boundary conditions * ; the instantaneous change of motion is then given by ( 21 ) . The Lagrangian Forms of the Equations . 16. Let a , b , c be the initial co - ordinates of ...
... determine a value of satisfying this equation and the proper boundary conditions * ; the instantaneous change of motion is then given by ( 21 ) . The Lagrangian Forms of the Equations . 16. Let a , b , c be the initial co - ordinates of ...
Page 20
... of t , the complete determination of p requires a knowledge of its value at some point of the fluid for all values of t . 26. A comparison of equations ( 2 ) with the 20 INTEGRATION OF THE EQUATIONS IN SPECIAL CASES . [ CHAP . II .
... of t , the complete determination of p requires a knowledge of its value at some point of the fluid for all values of t . 26. A comparison of equations ( 2 ) with the 20 INTEGRATION OF THE EQUATIONS IN SPECIAL CASES . [ CHAP . II .
Page 25
... determining the constant in ( 10 ) so that p = P ( the atmo- spheric pressure ) , when z = 0 , we have P Ρ = P + gz - 192 . P ( 13 ) . At the surface of the issuing jet we have p = P , and therefore q2 = 2gz ..... ( 14 ) , i.e. the ...
... determining the constant in ( 10 ) so that p = P ( the atmo- spheric pressure ) , when z = 0 , we have P Ρ = P + gz - 192 . P ( 13 ) . At the surface of the issuing jet we have p = P , and therefore q2 = 2gz ..... ( 14 ) , i.e. 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 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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