efficiently by averaging the resulting expression derived for the drag. 

 In terms of the total heads, defined by 



pg H_ = p_ + y p U^^, pg H = p + ^ p [(U_+u) Wh^^] (69) 



where g is the acceleration of gravity, (68) becomes 



"■II 



pg (H^-H)- ^ p [(U^+u)^-U„^-v^-w^] } dS (70) 



We now consider an equivalent irrotational velocity field (U_ + u ,v^ , 

 w^ ) , with pressure p , generated by a volume distribution of sources of 

 strength y in BLW, such that (u ,v ,w ) = (u,v,w) on T, the outer boundary 

 of BLW. We again apply the momentum theorem, to the flow within the same 

 control surface generated by this distribution of so-called Betz sources, 

 to obtain the expression for the force on the sources within the control 

 volume , 



D^ = -|p J [(VVHSS'l dS (71) 



the term corresponding to the difference in heads vanishing since the 

 field is irrotational. 



Another expression for the force on the Betz sources is given by the 

 Lagally formula 



/ ^<V 



D^ = - 4ttp y(UQ+u^) dx (72) 



28 



