T. =^pa^U^lng=- pa^U^lnsec— [65k] 



If L/a is small, using the series for cos and In from Section 33, 



° 24a2 / 



(For notation and method; see Section 34; Reference Love^° and Taylor. ^^ 



66. LAMINAS OR CYLINDERS AND SURFACES 



A lamina in other positions between rigid walls was studied, with reference to the lift 

 when there is circulation around it, by Rosenhead^^ and Tomotika,^^ ^nd more generally by 

 Tomotika and others, ^^~^*, and by Havelock.^^ When the lamina is centered but inclined at 

 an angle to the walls, with the circulation so chosen as to make the velocity finite at the 

 trailing edge, the lift is increased by the presence of the walls, largely because the necessary 

 circulation is itself increased. 



Cylinders of a certain shape between walls, including a first approximation to a circu- 

 lar cylinder, are discussed in Sections 46 and 47. A plate near a single rigid wall was stud- 

 ied by Villat,^° Raimondi,^* and Tomotika and others, ^2-65 ^nj^ ^j^j^ qjjq edge on the wall, 

 by Datwyler^^ and Tomotika and Imai.^^ The wall increases the lift, at least at small angles 

 of incidence. The effect of a neighboring free surface was studied by Tomotika and Imai.^* 



A circular arc near a rigid wall was treated by Jones, ^^ and, for the case of actual 

 contact, by Tomotika and Imai.''° A cylinder near a wall was discussed in general terms by 

 Villat.60 



Circulatory flow between a cylinder and a free surface was treated by Vitali.'^ 



CIRCULAR CYLINDERS 



67. SYMMETRICAL FLOW PAST A CIRCULAR CYLINDER; DIPOLE IN 

 A PARALLEL STREAM, OR INSIDE A COAXIAL SHELL 



w = viz + — j, U and a real constants, a > 0. [67a] 



From w = cf) + it// and z = x + iy, ,- 



^ = U \l+-\x, ip = ull- — jy, r = (a?2 + y2)V^ ^ [67b,c,d] 



148 



