C • STATISTICAL THEORIES OF TURBULENCE 



screen. At the same time, there is a side force in the plane of the screen 

 per unit area, given by 



S = Fe-lpU^ (24-2) 



Experiments by Schubauer, Spangenberg, and Klebanoff [95] at the 

 National Bureau of Standards (NBS) show that the coefficients Fe and 

 Ke are related for usual wire gauze screens. Dryden and Schubauer [96] 

 proposed the relation 



Fl> 4:Ktt 



T = OT (24-3) 



which agrees with experiments for Ke < 1.4. Taylor and Batchelor [83] 

 fitted the NBS data with the empirical formula 



^ = 2 - /-^ (24-4) 



B V^ + Kg 



which appears to be a reasonable approximation for 0.7 < Kg < A. 



Schubauer, Spangenberg, and Klebanoff also found that Kg/cos^ 6 can 

 be uniquely related to R cos 6, where R is the Reynolds number. This 

 means that the pressure drop depends essentially on the normal compo- 

 nent of the velocity. 



Theoretically, it is useful to introduce a "refractive index" a. If the 

 departing stream makes an angle with the normal to the screen, then 

 a = (t)/d. For small angles, 



S© 



This leads to 



a = l-lim(^:) (24-5) 



-^K 



S- K 

 1.1 



V^+K 



for K < 1.4 



(24-6) 

 for 0.7 < K <4: 



Dryden and Schubauer [96] found that the kinetic energy of turbu- 

 lence is reduced by the factor (1 + K)~'^ after passing through the screen. 

 This result does not distinguish between the longitudinal and lateral com- 

 ponents of the velocity. It has been verified by the more careful measure- 

 ments of Schubauer, Spangenberg, and ICebanoff for flow Reynolds num- 

 bers above a certain critical value. For lower Reynolds numbers, the 

 reduction factor is found to be lower. 



A theory developed by Taylor and Batchelor [97], however, predicts 

 different reduction factors for the longitudinal and the lateral compo- 

 nents. They also predicted a reduction of the turbulence level immedi- 

 ately in front of the screen. 



< 250 ) 



