B,30 • VELOCITY DISTRIBUTIONS IN JETS AND WAKES 



In this case 



D„ = 0.00196(a; + xo)Uo (30-9) 



According to Schlichting [96] the velocity at the center may be ex- 

 pressed by 



Uo = i- n /^l ^ (30-10) 



Here 



Kr = strength of jet = 27r / Wrdr = j DWl (30-11) 



Jo 4 



where D is the diameter of the nozzle and U^ is the jet exit velocity. By 

 means of Eq. 30-9 and 30-11, Eq. 30-10 may be written 



# = ^^ (30-12) 



Ue x^ oco 



D'^ D 



According to Hinze and van der Hegge Zijnen the numerical constant in 

 Eq. 30-12 turns out to be 6.39 on the basis of their observed axial dis- 

 tribution of velocity. 



When Uc given by Eq. 30-10 is substituted into Eq. 30-9, 



Du = 0.0153 VYr (30-13) 



In jets, as in wakes, the constant exchange coefficient makes the 

 calculated velocity approach zero too slowly in the outer regions. This 

 discrepancy is tolerated partly because it is in the region where the ve- 

 locity is low and partly because the reason for it is understood in terms of 

 intermittency. 



Since the exchange coefficient Z)„ is the turbulent kinematic viscosity, 

 it is interesting to compare it to ordinary kinematic viscosity p. For the 

 plane wake from a cylinder the ratio Du/v is found from Eq. 30-4 to be 



— = 0.0173 — (30-14) 



V V 



where U^d/v is the Reynolds number of the cylinder. A similar expression 

 may be found for the round jet by replacing Kr in Eq. 30-13 by Eq. 30-11. 

 The result is 



^ = 0.0153 2^EiR = 0.0135 -^ (30-15) 



If, in these two examples, d and D are both one inch and U^ in both 

 cases is 100 ft/sec, the Reynolds number for air at ordinary temperature 

 and pressure is about 4.9 X 10*. The two values of Du/v are then found 

 to be 850 and 660 for the wake and jet respectively. These figures serve to 



< 175) 



