541 



HYDRAULICS AND ITS APPLICATIONS 



low. Even though the stream may ro-expand to fill the buckets and the 

 wheel act as a pressure turbine, yet with the same pressure at exit from 

 the wheel, the pressure at the exit from the guides will be greater than 

 when running full, though not to the same extent as before, so that in 

 either case the volume of water passing the wheel is larger than might 

 be expected from a consideration of the gate opening. 



This action is well illustrated by the following results of tests carried 

 out by Mr. J. B. Francis on a mixed flow turbine, of which the. following 

 are the leading dimensions 1 : 



Outer diameter of runner, G feet. 

 Least diameter of runner, 2 feet 8 inches. 

 Width of guide passages, 13-1 inches. 

 Width of buckets, Z> 2 , 13-3 inches. 

 Measured area of outflow from guides, 

 9-88 square feet. 



a = 25. 



jS = 90. 



7 from 22 to 26. 



Number of guide vanes = 24. 



Number of bucket vanes = 25. 



t l 0-4 inches. 



Measured area of outflow from buckets, 9 - 5fi square feet. 



Again, friction losses in the wheel increase continuously with the speed, 

 and do not attain a minimum value simultaneously with the minimum 

 values of the losses by shock and by rejection of kinetic energy, so that, 

 although the expressions previously obtained for the efficiency, by neglect- 

 ing these losses, indicate that this is independent of the speed of rotation, 

 there will, in actual working, be one particular speed for any turbine 

 working under a given head that speed at which the sum of the various 

 losses forms the least proportion of the energy supplied by the water 

 for which the efficiency will be a maximum. 



Experiments by Professor Fliegner, of Zurich, 2 indicate that the loss at 

 entrance diminishes as the working head increases, and that its minimum 

 value does not occur for inflow without shock, but when the angle ft has a 

 value differing from the theoretical, the best angle being greater than the 

 theoretical for values of /3 less than about 105, and less than thfl 

 theoretical for values of /3 greater than this. 



1 Journal Franklin Institute, vol. 99, p. 249. 



2 Zeitschrift des Vereines Deutscher Ingenleure, vol. 23, p. 459. 



