GOVERNORS. 



On the Motion of a Liquid in a Tube revolving about a Vertical Axis. 



C. ir. Sitmenst Liquid Governor. Let p be the density of the fluid, k 

 the section of the tube at a point whose distance from the origin measured 

 iilong the tube is *, r, 0, z the co-ordinates of this point referred to axes fixed 

 with respect to the tube, Q the volume of liquid which passes through any 

 s<ction in unit of time. Also let the following integrals, taken over the whole 

 tube, be 



C ...................... (1), 



the lower end of the tube being in the axis of motion. 



Let ^ be the angle of position of the tube about the vertical axis, then 

 the moment of momentum of the liquid in the tube is 



(2). 



The moment of momentum of the liquid thrown out of the tube in unit of 

 time is 



~* s *~ 



where r is the radius at .the orifice, k its section, and a the angle between the 

 direction of the tube there and the direction of motion. 

 The energy of motion of the fluid in the tube is 



(4). 



The energy of the fluid which escapes in unit of time is 



The work done by the prime mover in turning the shaft in unit of time is 



7 I 1 I t 1 "Tf i **. 



_ dH 



dt-dt(d 



The work spent on the liquid in unit of time is 



<I\V d 



dt 



