Figure 175 — Streamlines produced by a plane lamina rotating about one edge. 

 (Copied from Reference 10.) 



The pressure can be found from Equation [lie] or [lid]. 

 A lamina bent sharply along its median line was studied by Sona. ^ 

 (For notation and method; see Section 34; Reference 1, Article 72; Reference 2, 

 Section 9.65; Zahm^^"* and Consiglio.^^^ 



CHANNELS 



107. FLOW PAST A SQUARE END OR AN OFFSET 



Let a stream of fluid, having a uniform velocity (J at infinity, flow past an obstacle 

 in the form of a two-dimensional semi-infinite rectangular box; let the box have a face of 

 width 2h perpendicular to U and two other faces extending to infinity in the direction of f/, 

 as illustrated in cross section in Figure 176, on the 2-plane. 



Let the a;-axis be taken in the median plane of the obstacle with the origin on its front 

 face. Then it is obvious from symmetry that a streamline follows the a;-axis to the box, 

 divides, and proceeds to infinity along both sides of the box. 



It suffices to determine the flow above the a;-axis; that below it is then the mirror 

 image in the axis of the flow above. A rigid boundary could, in fact, be inserted along the 

 a;-axis to the right of the box without disturbing the flow. Thus either half of the flow will 

 serve also to represent the flow past a plane wall with an offset in it of width h. 



The bounding streamline COBA constitutes an infinite polygon and can be transformed 

 into the real axis of a new variable t by the Schwarz-Christoffel method. The streamline 

 must be traced in the direction ABOC to make the area above it correspond to that above the 



262 



