KADIAL FLOW 79 



that the energy rendered available by the dying out of eddy motion is 

 more than equal to that absorbed in overcoming viscous resistance after 

 the throat is passed. 1 



With high velocities, however, the process of eddy formation goes on 

 after the throat is passed, part of the available pressure energy being 

 expended to this end, and H 3 is in consequence increased. At a suitable 

 velocity, a balance is obtained between the energy absorbed from P to B 

 in eddy formation and that made re-available by the dying out of eddies, 

 and in this case H 3 will equal HI. 



In every case, however, the head loss (H 2 -f H 3 ) is greater than HI, and 

 experiments show very clearly that, while it is possible to change pressure 

 head to velocity head without appreciable loss of energy, it is impossible 

 to change velocity head to pressure head by the reverse operation without 

 loss, except at velocities too low to be considered in practice. 



This is one important factor in the difference between the efficiencies 

 of centrifugal pumps and turbines. 



ART. 32. FLOW IN CONVERGING CHANNELS. BADIAL FLOW. 



Where flow takes place in a converging channel, the motion is steady, 

 and, neglecting viscosity, 2 the 

 energy throughout any stream 

 tube is constant, so that 



-. -j ^- + z = constant. p 



U~ 

 But for continuity of flow, if A = L. 



area of channel at some point FlG< 



where the velocity is v, 



A v = constant = A VQ 



where A and v are the area and velocity at some point distant x from 

 the point of convergence of the boundaries (Fig. 37). 



Putting A = k x we have v = ^, and if z is constant, i.e., if the 



x 



stream lines are horizontal, 



--c (1) 



1 Since the velocity across the section is unequal, the K. E. (2(wr 2 )) is greater than M& 

 where 5 is the mean velocity. Thus the equalisation of the velocities tends to increase the 

 apparent, though not the actual, K. E. 



2 For the viscous resistance in a converging channel, see " Phil. Mag.," July, 1909, p. 25. 



