558 HYDRAULICS AND ITS APPLICATIONS 



results, since the velocity of flow across the whole outlet area will not be 

 equal. This follows because of the reduced resistance to flow through 

 those elements which offer the shorter path to the water, and in which at 

 the same time, because of their shorter radial length, the resistance to 

 inward flow caused by the centrifugal action of the water, is least. Thus 

 the velocity of flow will be greater in those elements of the discharge 

 area which are at a greater distance from the centre. 



It thus becomes necessary for accurate results to treat each section as 

 a separate turbine with given inlet and outlet pressures, and so to 

 calculate the relative flow per unit area across each section. 



This involves very elaborate calculations, 1 and the more usual method 

 in practice is to determine the correct mean angle for the outflow at the 

 point of mean radius on the assumption that this outflow is uniform over 

 the whole section. 



AET. 149. IMPULSE TURBINE OF THE GIRARD TYPE. 



Here the pressure remains constant throughout the turbine, being 

 either atmospheric or that corresponding to the air pressure inside the 

 turbine casing, so that p 2 = PS. 



As in the pressure turbine, the work done by the water, assuming the 

 vanes designed to give no velocity of whirl at exit, is given by 



W 

 U = - - w 2 u 2 foot Ibs. per second. 



i/ 



The equation of energy 



ffg , W 2 2 +/ 2 2 _ p 3 / 3 2 W 2 Uy 



W^ 20 " W^ 2 "* g 

 now simplifies to 



w 2 2 +/ 2 2 -/ 3 2 = 2 w 2 MS. (1 



Writing / 3 = Ar/ 2 , this becomes 



W + (1 -- #)/* = 2 wa Ma- (2 



If / 2 =/s, i.e., k = 1, this reduces to w 2 = TT , and since *J ~w 



A 



= C v */ 2 g H' t where C v = '97 (approximately) 



1 For a mauiematical investigation into this matter the reader may consult an article 

 Professor Lorenz, Xeitsckrift des Vereines Deutscher Ingenieure, October, 1 ( JU5 (p. 1670),: 

 Zur Ikeorie der Francis Turbine/t, Fritz Oesterien. Berlin. Julius Springer. 



