320 



Mr. J. L. Woodbridge on Turbines. 



will A B be the velocity of the stream relative to the wheel. 

 Now if A B does not coincide with the tangent to the vane at 

 A, the stream cannot suddenly be made to change its direction 

 into that of the vane, or float : and the water, by cushioning in 

 the angles, will make its own angles, as roughly shown in fig. 3. 

 Fig. 2. Fig. 3. 



'f 



It is impossible, either practically or theoretically, to determine 

 the new angles, and probably they are not constant ; neither 

 is it possible to determine the loss of energy due to eddying ; 

 w r e therefore make the hypothesis that the final direction of 

 the guide-plates, the initial direction of the vanes, the angular 

 velocity of the wheel, and the velocity of the flow, are so 

 related that the water on leaving the guide-plates shall 

 coincide in direction with the initial elements of the vanes. 

 Any three of the four quantities above mentioned being fixed, 

 the fourth becomes known by this relation. We will leave 

 the angle of the guide-plates to be determined later. 

 Let 



V = the actual velocity of the water on leaving the guide-plates, 

 v^the velocity relative to the vane, as before. 



Then Y must be the resultant of <op x Fig. 4. 



and v 1} and we have 



V 2 = V + 



*>v 



2v 1 cop 1 cos Yi. (10) 



From Bernoulli's theorem we have for 

 the flow of water in the head-race the 

 equation 



p. , *_*. y2 



z& 



+D 



4 + v 



(11) 



t) being the mean height of the surface 



of the water in the reservoir above the 



wheel. We thus have two equations, (10) and (11 



ducing one new unknown quantity. 



;, intro- 



