36 



or the momentum equation for axisymmetric flow (<5«r ), 



d(r w g) 

 dx 



r jtt h + i t 



U d* 



[82b; 



pU< 



and the moment -of -momentum equation which holds for both two-dimensional and 

 axisymmetric flows (6 <<r ), 



fl dH _ H(H+l)(H 2 -l) dU . , „ 2 .. , 



dx 



U dx 



-(f) -"-ii^ni. 



where 



and 



" U(h+dJ 



* [83] 



[42; 



H„-1 



VV 1 



[43] 



The variation of ( y / y o) H o +1 with H and H is shown in Figure 9- The varia- 

 tion of H with R , shown in Figure 11, is given by Reference 15 as 



log 10 H n = 0.5990 - 0.1980 log R + O.Ol89(log 10 R ( ,) ; 



>io "0 

 The relation between I and H is 







H. 



H„ + l 



1 + 



0.0378 V52.9 log 10 H -4.l8 



Hf 



1 



[58; 



[78; 



Figure 14 shows I as a function of R 9 . The variation of T /pU 2 with R fl , 





 Figure 10, for the Schoenherr formula is 



T w 0.01466 



,U 2 log 10 (2Rj[y log 10 (2R J +0.4343] 



[57 



The variation of U and dU/dx with x will be specified for a particular problem 

 and may be obtained either by pressure measurements or potential-flow 

 calculations . 



The momentum and moment-of -momentum equations are solved for 0(x) 

 and H(x) as a pair of simultaneous differential equations, usually by numer- 

 ical methods involving step-wise integration. The initial conditions for 6 (x) 

 and H(x) are imposed by the physical conditions of the problem such as the 



