. Memoirs and proceedings of the Manchester Literary & Philosophical Society . e fourth. If the intensity of the vortex be defined asthe velocity at a given radius, this action willevidentl)^ vary as the square of the intensity. (3) The fact that, since the velocity of the water variesinversely as the distance from the centre, there isa relative motion of water and solid, in thedirection of revolution, over that portion of theperiphery marked nba in the Figure, and, in theopposite direction, over the periphery marked causes the body to rotate about its own axisrelatively to the surrou
. Memoirs and proceedings of the Manchester Literary & Philosophical Society . e fourth. If the intensity of the vortex be defined asthe velocity at a given radius, this action willevidentl)^ vary as the square of the intensity. (3) The fact that, since the velocity of the water variesinversely as the distance from the centre, there isa relative motion of water and solid, in thedirection of revolution, over that portion of theperiphery marked nba in the Figure, and, in theopposite direction, over the periphery marked causes the body to rotate about its own axisrelatively to the surrounding zvater^ in the oppositedirection to that of its revolution around the 14 Gibson, Bodies floating in a Free or a Forced Vortex. centre of the vortex. Since, however, in virtue ofits revolution, the object makes one rotation perrevolution in the direction of revolution, theabsolute direction of rotation will usually be in thesame direction to that of revolution. This rotation, relative to the surrounding water, hasindirectly, an important bearing on the behaviour of the. object. To realise this it must be remembered that,other effects neglected, the body tends to gravitate tothe centre of the vortex, in virtue of the inward spiralflow. But over the periphery aba (Fig.) the velocity ofthe surrounding fluid is greater than that of the body, andin virtue of the rotation of the body, this flow will bedeflected inwards towards the centre of the the force accompan\ing the change ofmomentum of this passing stream of water will have anmctivard radial component. Similarl), since the portionacd of the body is moving past its contiguous fluid this Manchester Memoirs, Vol. Iv. (1911), No. 7. 15 portion of the wake will be deflected outivards by therotation,* and the corresponding force on the body will,in consequence, have an inward radial component. As,however, the relative velocity is greater over the portionsof the body nearer the centre of the vortex, the result
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