culate the momentum area of the boundary-layer flow for each of its stages in order to deter- 

 mine the resulting drag of the body. 



PRESSURE DISTRIBUTION ALONG THE BODY 



Before any boundary-layer calculations can be performed for the body of revolution 

 whose drag is to be determined, it is necessary to have on hand the distribution of pressure p 

 along the body, which in non-dimensional terms is usually presented as 



P - P« 



2 



-(t/ 



[8] 



Here p^ is the pressure of the undisturbed stream far ahead, and V is the velocity at the outer 

 edge of the boundary layer. 



Where no experimental values of pressure distribution are available, recourse can be 

 had to methods for calculating the potential flow past the body which involve the solution of 

 the Laplace equation for arbitrary boundary conditions. Such methods, which are reviewed 

 briefly and evaluated in Reference 3, are, in general, numerically arduous and difficult to 

 apply to bodies of arbitrary shape. Recently, Landweber^ developed an accurate method, well 

 suited to automatic calculating machines, in which a special iteration formula is employed in 

 solving the resulting Fredholm integral equation of the first kind. A faster method, giving, 

 however, only approximate results, is that of Young and Owen'* which involves interpolation 

 among tabulated values of Legendre polynomials. 



For the original profile of the body of revolution the calculated pressure distribution 

 for potential flow agrees closely with measured values over most of the length of the body, 

 the greatest discrepancy appearing neafthe tail because of the displacement effect of the 

 boundary layer. A closer result can be obtained, however, by repeating the potential-flow cal- 

 culation for a somewhat altered body consisting of the original contour and an added thickness 

 based on the displacement effect of the boundary layer. The added displacement thickness in 

 the y-direction normal to the surface for a body of revolution in axisymmetric flow, as shown 

 in Figure 2, is obtained by equating the total flow retarded in the boundary layer of thickness 

 S to the amount subtracted from the potential flow of thickness a* or 



8 



2 7T {U -0) rdy = 2Tr(U-u)Tdy 



\rdy= J (l-|)rc^,.A* 



[9] 



[10] 



