A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 4
... give pda dy dz X. The pres- sure on the yz - face which is nearest the origin will be ultimately - 12112123 dp dda ) dy dz , that on the opposite face ( p + dp dr ) dydz . The difference of these gives a resultant dp - dx dx dxdydz in ...
... give pda dy dz X. The pres- sure on the yz - face which is nearest the origin will be ultimately - 12112123 dp dda ) dy dz , that on the opposite face ( p + dp dr ) dydz . The difference of these gives a resultant dp - dx dx dxdydz in ...
Page 6
... give together dxdydz . Calculating in the same way dx the parts due to the other faces , we find av It = du dv dw + ( du + dx dy du ) dxdydz . Since we have also V = dxdydz , ( 6 ) becomes ( du + dv dw + dz = ( 7 ) , Ət др du + P dx dy ...
... give together dxdydz . Calculating in the same way dx the parts due to the other faces , we find av It = du dv dw + ( du + dx dy du ) dxdydz . Since we have also V = dxdydz , ( 6 ) becomes ( du + dv dw + dz = ( 7 ) , Ət др du + P dx dy ...
Page 9
... give a gain of - d . Qu dx dx dy dz per unit time . Calculating in the same way the effect of the flow across the ... gives the equation of continuity in the form ( 8 ) . Next , let us take the change of momentum , making Q = pu , the ...
... give a gain of - d . Qu dx dx dy dz per unit time . Calculating in the same way the effect of the flow across the ... gives the equation of continuity in the form ( 8 ) . Next , let us take the change of momentum , making Q = pu , the ...
Page 10
... gives + d.pu d . pu2 , d . puv + dt dx dy d . риго + = pX- dp . ( 17 ) . dz dx Performing the differentiations , and simplifying by means of the equation of continuity , we are led again to the first of equations ( 2 ) , and in like ...
... gives + d.pu d . pu2 , d . puv + dt dx dy d . риго + = pX- dp . ( 17 ) . dz dx Performing the differentiations , and simplifying by means of the equation of continuity , we are led again to the first of equations ( 2 ) , and in like ...
Page 12
... give the whole history of every particle of the fluid . The velocities parallel to the 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 ...
... give the whole history of every particle of the fluid . The velocities parallel to the 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 ...
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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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