Mathematical and Physical Papers, Volume 1University Press, 1880 - Hydrodynamics |
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Page 8
... Hence for the whole motion just after impact v ( U + U ) = yU = -2w , which satisfies the equation of steady motion ( 10 ) ; and as the condition at the boundary , namely that the fluid shall slide along it , is satisfied , being ...
... Hence for the whole motion just after impact v ( U + U ) = yU = -2w , which satisfies the equation of steady motion ( 10 ) ; and as the condition at the boundary , namely that the fluid shall slide along it , is satisfied , being ...
Page 9
... , d dy dx dU , d + $ ' ( U12 ) ( at dy dx or , dx dU d_dU , d ) ( dU , dU3 ) 1 1 dx dy da 1 dy + = 0 ; dy Pp ” ( U1 ) + Q & ′ ( U1 ) = 0 , suppose . Hence , as before , if we express y in ON THE STEADY MOTION OF INCOMPRESSIBLE FLUIDS . 9.
... , d dy dx dU , d + $ ' ( U12 ) ( at dy dx or , dx dU d_dU , d ) ( dU , dU3 ) 1 1 dx dy da 1 dy + = 0 ; dy Pp ” ( U1 ) + Q & ′ ( U1 ) = 0 , suppose . Hence , as before , if we express y in ON THE STEADY MOTION OF INCOMPRESSIBLE FLUIDS . 9.
Page 10
... Hence , the velocity may be any function of the distance from the centre . It is evident that we may conceive cylindrical shells of fluid , having a common axis , to be revolving about that axis with any velocities whatever , if we do ...
... Hence , the velocity may be any function of the distance from the centre . It is evident that we may conceive cylindrical shells of fluid , having a common axis , to be revolving about that axis with any velocities whatever , if we do ...
Page 11
... Hence the velocity must be approximately constant ; and therefore , the fluid which came from the first vessel , instead of spreading out , must keep to a canal of its own of uniform breadth . This is found to agree with experiment . Hence ...
... Hence the velocity must be approximately constant ; and therefore , the fluid which came from the first vessel , instead of spreading out , must keep to a canal of its own of uniform breadth . This is found to agree with experiment . Hence ...
Page 12
... Hence the pressure consists of two parts , the first , pV , the same as if there were no motion , the second , the part due to the velocity . Now the velocities are given by equation ( 14 ) , and by the three equations which result on ...
... Hence the pressure consists of two parts , the first , pV , the same as if there were no motion , the second , the part due to the velocity . Now the velocities are given by equation ( 14 ) , and by the three equations which result on ...
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according angle apply approximation arbitrary axes axis become infinite Cambridge Philosophical Society canal centre co-ordinates condition Consequently considered constant convergent series corresponding cosines cylinder Demy Octavo denote depth determined direction discontinuous divergent series dx dy elastic equal equation essentially convergent ether exact differential expansion expression finite force formula friction function given h vanishes Hence homogeneous function horizontal increases inertia integral length limit molecules moment of inertia observed obtained Octavo order of approximation oscillation oscillatory waves paper parallel parallelepiped particles perpendicular plane Poisson positive pressure quantities ratio rectangular refracting respect result satisfied shew shewn sines solid solitary wave sphere St John's College suppose surface tangential theorem theory tion variables velocity of propagation wave motion whence zero ηπα аф
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