CHAPTER XV 



Theory of Turbine Design Design of Stand Pipes. 



ART. 141. THEORY OF TURBINE DESIGN. 



THE turbine system, as a whole, may be divided into the supply pipe, 

 the turbine itself, and the discharge pipe. Losses of head are experienced 

 in each branch of the system, so that if 77 be the total difference of level 

 between open head and tail-race, the head available for doing work on 

 the turbine will be less than H by the amount necessary to overcome the 

 frictional and other losses in the supply and discharge pipes. 



The loss due to this cause is approximately proportional to the lengths 

 of the pipes and to the square of the velocity of flow, and its relative 

 importance diminishes as the gradient of the pipe line and its sectional 

 area are increased. Theoretically, by making the pipes of sufficiently 

 large area the loss may be made quite negligible. This increase in area 

 is, however, accompanied by a corresponding increase in the first cost, 

 and it appears to be fairly well agreed that in practice it does not pay to 

 reduce the pipe line velocity below from 6 to 8 feet per second, the value 

 to be adopted increasing with the gradient and with the head. 



In a large power plant where the head is high and the penstock direct, 

 this velocity may be increased without serious proportional loss of head 

 up to a maximum of about 16 feet per second. 



If, in any type of turbine, v be the velocity of the supply water at its 

 exit from the guide vanes, and if a be the angle between the guide vanes 

 and the direction of motion of the wheel at the point of entry, v may b( 

 resolved into two components ; v sin a, perpendicular to the direction 

 motion of the vanes, which is usually termed the velocity of flow, an 

 v cos a parallel to this direction, which is termed the velocity of whir 

 Throughout the following discussion the velocity of flow will be denote 

 by /, and that of whirl by w, Thus in a radial-flow turbine / is radifl 

 and w tangential to the wheel, while in an axial-flow machine / is paralk 

 to the turbine axis and w is in the plane of the wheel. 



In virtue of the velocity of whirl, the supply water possesses momei 

 turn in the plane of the wheel, and it is the change in the moment of th 

 momentum about the axis of the wheel during the passage of the wat< 



