where t = tanh 
1 s,ts Go) 
is the value of t at the point of reattachment, then the radius 
of the jet center line is derived from 
ot /te -1) (es) 
r/b 
2 30 
where t,and 8 are determined from the following equations: 
2 
D/b o(1/t,-1)(1-Cos 8) _— (hoG) 
e 30 
and 
3} 
Cosmen =e S/2. t,-1/2 ty (A-7) 
The half width of the jet at the reattachment point, i.e., y, 
can be easily derived from Equation A-4 and is 
y,/d, = se S tanh ae (A-8) 
Further, the distance of the reattachment point from the plane 
of the nozzle is 
o(1/t7-1) Sin 6 tanh’ 't, 
Se vest |) ee (A-9) 
Rio oe ae Sin 0 
Finally, the mean pressure within the separation bubble is computed 
by 
30 (A-10) 
Poy = Jip 
B o(1/t@-1) 
oO 
A wall attachment element can be designed using Equations (A-1) 
through (A-9). 
However, to use these equations conveniently, it is required 
that the flow parameters XR/bo> 1S//Doys ¥1/by and 8 be known as 
functions of the pre-determined parameter Dba These equations are 
complex and can not be expressed explicitly in terms of D/by alone. 
27 
