B,32 ■ EFFECT OF SURROUNDING AIR ON JETS 



constant be evaluated by experiment, and for this purpose existing data 

 for still surrounding air were used. Szablewski's method indicates some- 

 what greater effects, but it is difficult to judge the reliability of these 

 methods due to the basic assumptions and approximations made in the 

 solutions. No attempt will be made here to reproduce the developments 

 and final formulas, all of which tend to be cumbersome. Squire and 

 Trouncer achieved some simplification by arbitrarily adopting a cosine 

 velocity profile which for the fully developed jet takes the form 



^^ = i(l+cos.i:) (32-1) 



where Ui is the velocity of the surrounding stream, U^ the velocity on 

 the jet axis, r the radial distance from the axis, and fi the radius of the 

 jet boundary. 



We turn next to experiment, and here we find a comprehensive in- 

 vestigation conducted by Forstall and Shapiro [124\ aimed at testing the 

 analytical formulation of Squire and Trouncer and additionally com- 

 paring mass transfer and momentum transfer. For obtaining the mass 

 transfer 10 per cent by volume of helium was added to the jet as a tracer. 

 Values of Uo up to 225 ft/sec and values of Ux up to 90 ft/sec were used. 

 Velocity ratios Ui/Uo ranged from 0.2 to 0.75. 



Velocity and concentration profiles downstream from the end of the 

 potential region could be closely represented by a formula of the type of 

 Eq. 32-1. The assumption of this formula by Squire and Trouncer was 

 therefore well justified. The profiles remained substantially similar at all 

 values of x and were independent of the velocity ratio Ui/Uo. 



In order to avoid the uncertainty in specifying the extremes of the jet, 

 the size parameters Vmv and fmi were adopted, where r^v is the radius 

 where the velocity is the mean of its value on the axis and in the outside 

 stream, and rmj is the radius where the concentration is |- the concen- 

 tration on the axis. Expressing these in terms of the diameter of the 

 nozzle D the rate of spreading with x/D was found to be greater for 

 concentration than for velocity. A turbulent Schmidt number of about 

 0.7 was indicated (compare Art. 29). The experiments checked the law 

 of jet divergence derived by Squire and Trouncer. 



Both concentration and velocity were found to decay inversely with 

 x/D. In general, concentration showed more of a drop than did the ve- 

 locity, but the difference in behavior was small. The inverse law amounts 

 to a faster decrease with x/D than that predicted by the Squire and 

 Trouncer theory, although the theory gives the general order of magni- 

 tude of the center line properties. 



Forstall and Shapiro give the following empirical formulas for the 

 round jet in a surrounding stream of equal density to serve as rough 

 rules for the velocity field : 



( 181 > 



