27 



This analysis shows that although a small change in a may not affect the pressure minimum 

 appreciably, it may produce changes in the shape of the pressure distribution curve. 



The error introduced by a small mound or depression in a body may be approximated by 

 the two-dimensional flow over the arc of a circle extending from + c to - c on the x axis. The 

 complex potential for this flow is given by*^ 



2ci Un ^ + iv 

 w= ? cot [35] 



where 



^ + iri 

 z = X + ly = ic cot [36] 



1 

 The stagnation streamline is obtained by letting ^ = 2 nn- over the arc of the circle and ^ = 



on the plane. The shape of arc is determined by the parameter n, with n = 2 representing flow 



over a flat plate, 71 > 2 representing flow over a depression, and n < 2 representing flow over 



a mound. 



The curves tf = constant are another set of circles othogonal to the first set and with 

 centers on the x axis. At the center of the arc a; = 0, r; = 0, and at the edges x = ±c, rj = +00. 



For small mounds or depressions where the height t is small compared with the half 

 width c 



^= =rr±-^ [37] 



2 c 



Equation [37] may be used to determine n. 



The complex velocity over the arc of a circle may be found by differentiating Equation 

 [35] with respect to s 



^ + ir] 

 4C/o /sin— |— \2 



^ Sin ^5— 

 The square of the resultant velocity is then 



'"I + *y 16 /cosh 7?-COS ^ 



'^o cosh cos — 



n n 



[38] 



[39] 



