A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 30
... curve , returning to the point whence it started , is said to be many - valued or cyclic . The theory of many - valued velocity - potentials will be discussed in the next chapter . 36. Example 5. A mass of liquid filling a right ...
... curve , returning to the point whence it started , is said to be many - valued or cyclic . The theory of many - valued velocity - potentials will be discussed in the next chapter . 36. Example 5. A mass of liquid filling a right ...
Page 34
... curve , or circuit , the value of the integral is called the ' circulation ' in that circuit . We denote it by I ( ABCA ) . If in either case the inte- gration be taken in the opposite direction , the signs of will be reversed , so that ...
... curve , or circuit , the value of the integral is called the ' circulation ' in that circuit . We denote it by I ( ABCA ) . If in either case the inte- gration be taken in the opposite direction , the signs of will be reversed , so that ...
Page 35
... curve ) . For , in the sum in question , the flow along each side common to two elements Fig . 2 . comes in twice , once for each element , but with opposite signs , and therefore disappears from the result . There remain then only the ...
... curve ) . For , in the sum in question , the flow along each side common to two elements Fig . 2 . comes in twice , once for each element , but with opposite signs , and therefore disappears from the result . There remain then only the ...
Page 36
... curve . In these formulæ the quantities l , m , n are the direction - cosines of the normal drawn always on one side of the ... curves , provided the integration in the second member be taken round each of these in the proper direction ...
... curve . In these formulæ the quantities l , m , n are the direction - cosines of the normal drawn always on one side of the ... curves , provided the integration in the second member be taken round each of these in the proper direction ...
Page 38
... curves . 43. The function with which we have here to do is , together with its first differential coefficients , by the nature of the case , finite , continuous , and single - valued at all points of the region considered . In the case ...
... curves . 43. The function with which we have here to do is , together with its first differential coefficients , by the nature of the case , finite , continuous , and single - valued at all points of the region considered . In the case ...
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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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