EXAMPLES 99 



water in a centrifugal pump fitted with a Vortex Chamber. Here the 

 water in the impeller forms a forced vortex with outward radial flow, 

 while when free of the vanes an approximation to a free spiral vortex is 

 formed, and the pressure increases as the velocity diminishes outwards. 



Certain properties of the free vortex are of interest. If a film of oil be 

 formed on the surface, owing to its density being less than that of water 

 this at once approaches the axis of rotation and disappears down the 

 funnel of the vortex. The same thing happens to any small floating 

 body. If of moderate dimensions, however, the portion nearer the axis 

 of rotation is in a region of higher velocity than those portions further 

 removed, and a series of frictional forces is thus called into play, acting 

 on the body, which forces are greater as the points at which they act are 

 nearer the axis of rotation. The effect 

 of this is to produce a rotation of the 

 body about some point near its outer 

 edge, and away from the centre of the 

 vortex. The body may be thus alter- 

 nately attracted to and repelled from \ * 

 this centre, the action being repeated FlQ 61 ._^ mpound Vortex> 

 as long as the vortex is in existence. 



A large floating body destroys the funnel in its upper part, and, if 

 air is prevented from entering through the exit, in the lower part 



also. 1 Since in the floating body v x r, while in the liquid v oc , this, 



by friction, tends to destroy the vortex motion of the upper layers of 

 liquid, and, by viscosity, also of the lower layers. 



The formation of a vortex in a discharging vessel increases the time of 

 discharge by diminishing the effective area of the orifice, and by reducing 

 the inclination of the issuing particles to the plane of the orifice. Experi- 

 ments by the author showed that when discharging water under heads 

 varying from 8 to 12 inches in a free spiral vortex, the coefficient of 

 discharge was sensibly independent of the head and had a value '287 for 

 a 1-inch orifice and '178 for a 1^-inch orifice. When no vortex formed, 

 the coefficient was '62. 



EXAMPLES. 



(1) In a 12-inch Venturi meter the throat diameter is 4 inches. Taking 

 C to be constant = '982, determine the difference of head at the entrance 

 and throat when discharging 



1 For a full account of such phenomena, a paper by the author " Memoirs, Manchester Lit. 

 and Phil. Soc.," 1911 may be consulted. 



H 2 



