B • TURBULENT FLOW 



The mixing zone between two uniform streams of velocities Ui and U% 

 and the plane jet were treated on the basis of constant exchange coefficient 

 by Gortler [127]. Since this work has been well reviewed by Schhchting 

 [96], only selected results are repeated here. The calculated velocity profile 

 of the mixing zone is in very good agreement with experiment. The calcu- 

 lated distribution of axial velocity in the plane jet is also in good agree- 

 ment with experiment except in the outer regions where the calculated 

 profile approaches zero too slowly. The formula for the plane jet is 



C/=^^^(l-tanh^^) (30-5) 



where a = a free constant to be determined by experiment, 



y 



rt = a — 



X 



/ + 00 

 U^dy 



The velocity at the center Uc is given by 



It must be assumed in these formulas that x is the distance from the 

 point where the jet appears to originate. Schlichting quotes Reichardt's 

 experimental value of a as equal to 7.67 and Du as given by 



Du = 0m7y^U, (30-7) 



where y^ is the value of y where U/Uc = ^. 

 It follows from Eq. 30-5, 30-6, and 30-7 that 



£)„ = ^ 0.037 -^ \/Ki 



Du = 0.0102 \/K^ (30-7a) 



As mentioned in Art. 29, the adaptation of the laminar-type solution 

 for the round jet was investigated by Hinze and van der Hegge Zijnen. 

 Their expression is 



^ 1 (30-8) 



U. 



0+0 



where t?, = r/(x -\- xo) 



xq = virtual origin which turned out to be 0.6 times the orifice 

 diameter 

 {x -i- Xq) = over-all distance from point where jet appears to originate 



ao = const = 0.00196 



< 174 ) 



