A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 3
... denote the intensities of the stresses faces ABC , PBC , PCA , PAB , respectively , of the tetrahedron PABC . If A be the area of the first - mentioned face , the areas of the others in order are l △ , mA , nA . Hence if we form the ...
... denote the intensities of the stresses faces ABC , PBC , PCA , PAB , respectively , of the tetrahedron PABC . If A be the area of the first - mentioned face , the areas of the others in order are l △ , mA , nA . Hence if we form the ...
Page 4
... denote by ƏF It a It the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the position ( x + udt , y + vdt , z ...
... denote by ƏF It a It the symbol being used to express a differentiation following the motion of the fluid . At the time t + dt the particle which at the time t was in the position ( x , y , z ) is in the position ( x + udt , y + vdt , z ...
Page 5
... denote the volume of a moving element of fluid , we have , on account of the constancy of mass , a.pv Ət = 0 ap √ + P at av = 0 ..... . ( 6 ) . or at Now the rate of increase of volume of a moving region is evid- ently expressed by the ...
... denote the volume of a moving element of fluid , we have , on account of the constancy of mass , a.pv Ət = 0 ap √ + P at av = 0 ..... . ( 6 ) . or at Now the rate of increase of volume of a moving region is evid- ently expressed by the ...
Page 9
... denote the measure , estimated per unit volume , of any quantity connected with the properties of a fluid , and let us cal- culate the rate of increase of Q in a rectangular space dady dz having its centre at ( x , y , z ) . This is ...
... denote the measure , estimated per unit volume , of any quantity connected with the properties of a fluid , and let us cal- culate the rate of increase of Q in a rectangular space dady dz having its centre at ( x , y , z ) . This is ...
Page 10
... denotes the resultant velocity √ ( u2 + v2 + w2 ) , V the potential energy per unit mass with reference to the ... denote a point of the fluid infinitely close to the surface F = 0 ; and let A , B , C be the points in which this ...
... denotes the resultant velocity √ ( u2 + v2 + w2 ) , V the potential energy per unit mass with reference to the ... denote a point of the fluid infinitely close to the surface F = 0 ; and let A , B , C be the points in which this ...
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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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