w j] 



420 Mr. Ewart on the Reaction of effluent Water ^ 



scended from B to C, and has been brought to rest. But the 

 reaction is = a x 2 BC, and this multiplied by 2 BC, the space 



through which it has acted, gives a x 2BCi 2 for the amount of 

 the moving force produced, which is exactly the quantity of 

 moving force necessary to raise the column a x 2 BC to the 

 height BC, and to project it with the velocity 2 BC. For, a 

 moving force = a x 2 BC x BC will raise that column from C 

 to B, and an equal moving force will generate the velocity 

 2BC in the same column, therefore 2a x2BC x BC=« x 2BCf 

 is the whole moving force necessary to restore that column to 

 the place and condition in which it was before it began to de- 

 scend; and as no moving force has been expended in pro- 

 ducing change of figure, that quantity of moving force must 

 be found in the reaction of the water through the space which 

 the vessel has moved while the water descended and was 

 brought to rest. 



Upon the same principle an easy 

 and simple explanation may be given, * l 8' 2# 



I apprehend, of the action of the hy- 

 draulic machine called Barker's Mill. 

 Let AB (fig. 2.) be the perpendicular 

 tube, and BC the horizontal arm ; let 

 v express, in feet per second, the ro- 

 tatory velocity of the arm at the ori- 

 fice C, and let the water be supposed 

 to issue with the velocity due to the 

 pressure*. Putg = 16^ feet. 



If BC be a cylindrical tube, and 

 if q represent the quantity of water 

 it contains from B to C, the centrifugal pressure upon a 



section of the arm at C, will be ^ BC ; and whatever the 



length BC may be, the diameter remaining the same, q being 

 as BC, the centrifugal pressure at C will always be as w 2 ; and 

 it will be equal to the pressure of a perpendicular column of 



water whose height in feet is wp Then if h express in feet 



the height AB of the water in the vertical tube, h + -^- will be 



the whole pressure at C ; and if a express in feet the area of 



the most contracted section of the orifice, 2a (h -f —J will 



* It is here understood that the areas of the sections of the perpendicular 

 tube and of the horizontal arm shall be indefinitely large when compared 

 with the area of the orifice. 



express 



