In applying (83) , total head tubes which measure a total head H , 



m 



;iven by 



pg H^ = p + y p [(Uq+u)^+A(v^4iv^)], < a < 1 (84) 



where A is a calibration constant, (see Reference [9]), and velocities 



r 2 1^/2 



are used for H and u. In terms of H and u , with the small difference 



m m 



between u and u neglected in higher-order terms, (83) becomes 



J 



D = ^'^ I [2g(H -H ) + (u -u )(u^-Hi -2u^) 



,-/., I (Jm Imlml 



-v^^-w^^+A(v^-h^^)] dS (86) 



When the wake is turbulent, the mean value of D, obtained by replacing 

 (u,v,w) by (u+u' ,v+v' ,w+w' ) and averaging, where (u',v',w') denote the com- 

 ponents of the turbulent velocity fluctuations, becomes 



D = ^''^ r2g(H -H ) + (u^-u^)(u^+u -2u )-v/-w^^ 



I_u/UJL On> Imlml 11 



^l/"0 A 



,2^„2, „,2^, ,„,2^„,2^1 



+A (v +w ) -u' +A (v' +w' ) dS (87) 



where H and u now refer to their mean values. The Reynolds stress terms 



mm ■' 



2 



combine into (2A-l)u' for isotropic turbulence, and would hence be 



32 



