PRINCIPLES OF NAVAL ENGINEERING 



In other words, maximum work is obtained 

 from a reversing blade when the blade velocity 

 is exactly one-half the absolute velocity of the 

 steam at the blade entrance.^ The maximum 

 amount of work obtainable from a reversing 

 blade is twice the amount obtainable from the 

 flat vane shown in figure 12-3. 



In actual turbines, it is not feasible to 

 utilize the complete reversal of steam in the 

 blades, since to do so would require that the 

 nozzle be placed in a position that would also 

 be swept by the blades— an obvious impos- 

 sibility. Furthermore, if the steam entered 

 the blade tangent ially it would not be carried 

 through the turbine axially (longitudinally). How- 

 ever, it is only the tangential component of the 

 steam velocity that produces work on the tur- 

 bine blades; hence the nozzle angle is made as 

 small as possible. 



As we know, the work done on the blade must 

 equal the total energy entering minus the total 

 energy leaving. The velocity diagram for an 

 impulse turbine shown in figure 12-5 provides 

 a way of determining the work done on the 

 blade in terms of the various velocities and 

 angles. 



The tangential component (which is the only 

 component that produces work) of the velocity 

 of the entering steam is 



Vj cos a 



which is also equal to 



Vb + Ri cos b 



The tangential component of the velocity of 

 the departing steam is 



from Vj^ cos a, the resultant velocity may be 

 expressed as 



Vj^ cos a - V2 cos c 



or, alternatively, as 



Rj cos b + R2 cos d 



Assuming a steam flow of W pounds per 

 second, 



and 



W 



W 



mass per second 



force 



Therefore, the force on the blade is 



W 

 F, = — (Ri cos b + R2 cos d) pounds 



__W (Yj^ pQg 3 _ y^ cos c) pounds 



Work is force through distance. There- 

 fore, the rate of doing work on the blade is 



Wkb = FfaVb 



= W(R^ c°^b+R2 cos d) Vjj foot-pounds 

 ^ per second 



= g-^'^i cos a - V2 cos c) Vjj foot- 

 pounds per second 



V2 cos c 



which is also equal to 



Vjj - R2 cos d 



Since entering and leaving velocities are 

 opposed to each other if V2 cos c is in the same 

 direction as V^ cos a, and supplementary to 

 each other if V2 cos c is in the opposite direction 



This statement assumes, of course, that the nozzle 

 Is tangential to the blades. In actual impulse turbines, 

 the maximum amount of work is done when the blade 

 speed is one-half the cosine of the nozzle angle times 

 the absolute velocity of the entering steam. 



NOZZLE V, 



"steam jet 



BLADES 



147.92 

 Figure 12-3.— Elementary impulse turbine. 



322 



