B • TURBULENT FLOW 



velocity at the center decreases as x~^. A similar procedure may be used 

 for the other cases, and the results are summarized for all in Table B, 27. 



Table B,27 



Width parameter a;"*. 

 Velocity at center a;~". 



The same results may be obtained by setting up integral relations for 

 the energy and using these with the momentum relations to determine 

 m and n. This procedure is illustrated in [94]. 



The diffusion of heat and other scalar quantities is also of practical 

 and theoretical interest. The equations of heat transfer, written for 

 assumptions consistent with those made for the equations of motion, are 

 as follows : 



Plane jet and 

 mixing zone 



Round jet 

 Plane wake 

 Round wake 



dx dy pCp dy 



dx dr pCp r dr 



U — = — ^ 



dx pCp dy 



U — = —- ^^^g) 

 dx pCp r dr 



(27-10) 

 (27-11) 

 (27-12) 

 (27-13) 



where T is the mean temperature, q is the rate of heat transfer in the 

 y ov r directions per unit area (see Art. 10), and Cp is the specific heat at 

 constant pressure. In proper terms the same equations hold for the trans- 

 fer of matter. Molecular diffusion is so slow compared to turbulent dif- 

 fusion that the transfer pan be regarded as due entirely to turbulent 

 motions. 



Again assuming similarity, and expressing it in analogous terms, Eq. 

 27-10, 27-11, 27-12, and 27-13, together with the fact that the same 

 amount of heat and matter must flow through each cross section, serve 

 to determine the form of spreading and the decrease of center temper- 

 ature or concentration as a function of x. These are the same as for the 

 velocity, but the absolute magnitudes are different. 



In all cases the origin of x is that point from which the flow appears 

 to originate with the same law from the beginning. The point is usually 

 found by extrapolating the experimental curves to a virtual origin. For 



< 162 ) 



