A Treatise on the Mathematical Theory of the Motion of Fluids |
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Page 30
... circuit round the origin , whereas a single - valued function would under the same circumstances return to its original value . A function which like the above experiences a finite change of value when the point to which it refers ...
... circuit round the origin , whereas a single - valued function would under the same circumstances return to its original value . A function which like the above experiences a finite change of value when the point to which it refers ...
Page 34
... 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 we have I ...
... 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 we have I ...
Page 35
... circuit on the plane yz , and therefore equal to 2ldS , where dS is the area of the circuit , and l , m , n the direction - cosines of the normal to its plane . The coefficients of n and give in the same way , on integration , 2mdS and ...
... circuit on the plane yz , and therefore equal to 2ldS , where dS is the area of the circuit , and l , m , n the direction - cosines of the normal to its plane . The coefficients of n and give in the same way , on integration , 2mdS and ...
Page 37
... circuit which can be filled up by a continuous surface lying wholly in the region , or in other words capable of being contracted to a point without passing out of the region . Such a circuit is said to be ' evanescible . ' Again , let ...
... circuit which can be filled up by a continuous surface lying wholly in the region , or in other words capable of being contracted to a point without passing out of the region . Such a circuit is said to be ' evanescible . ' Again , let ...
Page 39
... circuit constitute a tube , which may be called a ' tube of flow . ' The product of the velocity ( q ) into the cross - section ( σ ) is the same at all points of such a tube . We may , if we choose , regard the whole space occupied by ...
... circuit constitute a tube , which may be called a ' tube of flow . ' The product of the velocity ( q ) into the cross - section ( σ ) is the same at all points of such a tube . We may , if we choose , regard the whole space occupied by ...
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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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