General Stmtlartty Hypothests for Jet and Wake Flows 
which, because of the structure 
dv/a(x/,) meeiilee lv. ie (7) F(a] 
involves elliptical integrals and therefore cannot be solved in closed 
form. The main difficulties arise from the substituted terms for ug 
and dug/dy in Eq.8. In order to get at least an approximate solution 
of the problem, it seems reasonable to replace these terms by some 
less complicated expressions: 
By inspecting Eq.5, one can easily realize that there are 
two asymptotic cases included in the new similarity transformation, 
namely dU,,/U*<< 1.0 (strong jet flow) and U*/U,.«1l.0 (weak jet flow 
of the wake type). For these asymptotic cases, the postulated simi- 
larity of momentum reduces to mere similarity of defect velocity. 
= g(n) with n= y/f (12) 
which is equivalent to the conventional similarity assumption. If this 
expression is used along with Eq.5, Eq.8 becomes 
oo y j-l 0 
Th awe) 36) with tates (4:3) 
If solved simultaneously with Eq.9, this equation yields the general 
solutions 
* 
While this paper was prepared, Eq.11l1 was solved by a Runge- 
Kutta-procedure for various forms of the similarity function f(n). 
It was found that no inconsistencies arise from the introduction of 
the new similarity transformation (Eq. 5 in the integral form of the 
energy equation. Thus it can be concluded that Eq.5 is fully compa- 
tible with the governing equations. The numerical solutions display 
the same features as do the closed-form solutions, which are des- 
cribed in this paper. Full details will be given in a subsequent re- 
port. 
L291 
