Betz Method for Determining Viscous Drag 



Betz [5] and Landweber and Wu [6] use equivalent irrotational flows to 

 derive formulas for the viscous drag of a body in terms of measured values 

 of pressure and velocity at a transverse section of the wake. A refine- 

 ment of these derivations, in which additional wake characteristics are 

 taken into account, will now be presented. 



The body is taken at the center of a circular channel of large radius, 

 and is at rest in a uniform stream of velocity U in the positive x- 

 direction. The disturbance velocity components in a rectangular (x,y,z) 

 coordinate system are (u,v,w), and p denotes the pressure. 



Figure 9 



We select a control surface consisting of the transverse sections AB, 

 far ahead of the body, CD or S a moderate distance behind it, and the 

 portion of the channel wall lying between these sections. On the section 

 AB, designated S , the pressure is the constant p , and the velocity is 

 (U„, 0, 0). Application of the momentum theorem to this control surface 

 yields the expression for the body drag D, 



D = j (Pq-P- 



p [(Uq+u)^-Uq^]} dS 



(68) 



in which p is the mass density of the fluid. If the wake is turbulent, 

 Reynolds stresses will be present, but these can be taken into account most 



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