Figure 28 — Transformation w = 2^^^ 46 



Figure 29 — Transformation /(g) =96 + itp for two families of orthogonal curves 



(^ = constant and ip = constant 48 



Figure 30 — Definition of a complex integral 52 



Figure 31 — A closed path of integration 55 



Figure 32 — Two alternative closed paths of integration 55 



Figure 33 — Integration around two singular points Q, R 57 



Figure 34 — Schwarz-Christoffel transformation 58 



Figure 35 — Path past a singular point 59 



Figure 36 — Semicircular path past a singular point 61 



Figure 37 — A large semicircular path 62 



Figure 38 — Some infinite polygons 65 



Figure 39 — Plots of four hyperbolic functions 68 



Figure 40 — Flow net for uniform flow 74 



Figure 41 - Definition of V and a in Equation [35a] 75 



Figure 42 - Flow net in a right angle: w = Az 75 



Figure 43 — Flow net for a line dipole: w - /x/s 77 



Figure 44 - Definition of a , y^ y^ in Equation [37r] 78 



Figure 45 — Part of flow net for a line quadrupole; w = A/z^ 79 



Figure 46 — Streamlines in an angle of a = rr/S radians: u: - Az^ 80 



Figure 47 — Streamlines around a right angle a = 3n-/2, w = z ' 80 



Figure 48 - Symmetrical streamlines around the edge of a semi-infinite plane 81 



Figure 49 — Asymmetric streamlines around the edge of a semi-infinite plane 81 



Figure 50 — Flow net for a line source or vortex: tt = - /4 In 2 82 



Figure 51 — Symbols for source or vortex at (a,b) 84 



Figure 52 — Streamlines for a superposed line source and vortex 84 



Figure 53 — Variables for Sections 41-42 86 



Figure 54 — Flow net for equal line source and sink, etc 88 



Figure 55 — Streamlines for a vortex pair 89 



Figure 56 — Streamlines due to a Karman vortex train or " street" 90 



