The corresponding potential, obtained by integrating Equations [136k, 1], in which the 

 lower signs are to be taken if A = Aj, fi = A , and the components and magnitude of the velocity 

 are 



— [/(A^-A^) -aVlnX^ = Vx aUln{r+x), 



[143i] 



. =f/ -1 + 



2t 



17S = 



U 



2 r{r + x) 



q^ = V^ 1-- + 



2t{t + x) 



[143j, k, 1] 



On the solid, since t + x = K^ = a, q'^ = ^^(1 - a/2r). 



The excess of pressure over that at infinity is everywhere positive. On the solid it is 

 V - V^- paU'^/ir; on the a;-axis ahead of it, where r = x, 



2 U 4^2 



[143m] 



The streamlines are illustrated on half of a plane through the axis in Figure 240. The 

 streamlines shown are equally spaced in the uniform stream and correspond to equal increments 

 of ip/oj. The value of p - p^ at points along the axis and on the paraboloid is also shown, on 

 an arbitrary scale and for steady motion. 



(See Reference 2, Section 15.58.) 



^ Axis of Symmetry 



2 



Figure 240 - Symmetrical flow past a paraboloid of revolution. The pressure 



along the axis and over the paraboloid is also shown. The focus is at 0. 



See Section 143. 



377 



