Efflux from a two-dimensional vase with curved sides was treated by Cisotti;^^^ see 

 also Reference 2, Section 11.54. 



Deadwater or Wake in an Infinite Stream 



A "deadwater," that is a region occupied by stationary fluid or by gas at suitable 

 pressure, ahead of a concave angle was shown to be possible by Villat. ^^^' ^^'^ A similar 

 deadwater can occur ahead of a convex angle, in addition to the usual wake behind it, when a 

 stream is incident unsymmetrically. The extent of the deadwater is indeterminate; see Thiry,^^^ 

 Jaffe,^^^' ^^^ and Morton;^^^ see also Yokota. ^® The indeterminateness is perhaps no more 

 surprising than the arbitrariness in the direction of the incident stream; it may be supposed that 

 the size of the deadwater was fixed by the manner in which the flow was established in the 

 first place. 



The wake behind a lamina with a rim on the forward side was treated by Love, behind 

 a lamina with flaps folded back by Schmieden, ^^^ behind a curved lamina by Leathern,^'* 

 Cisotti,250 and Argeanicoff.^°3 



Deadwater regions on the sides of a rectangle immersed in a stream parallel to the sides 

 were described by Riabouchinsky,^^° who also gives values of the inertia coefficient. 



A deadwater extending from one plane lamina to another was also described by 

 Riabouchinsky.^^° When the laminas are oppositely inclined to the stream there is circula- 

 tion around them as a whole. 



The wake behind circular and elliptic cylinders placed in a uniform stream was studied 

 by Brodetsky^°° and by Ford,^°^ and for the circular case in further detail by Schmieden. ^^^' ^°^ 



The symmetrically disposed free streamlines behind a circular cylinder, on which the 

 velocity is the same as that in the incident stream, may separate from the cylinder at any 

 angular position from = 55° to = 120°, approximately, where 6 is measured from the stag- 

 nation line on the forward side. If they separate at 55 deg, they are concave toward the wake 

 throughout their course; at intermediate angles they are convex near the cylinder and concave 

 beyond; at the largest angle they are convex throughout and meet asymptotically at infinity; 

 see Figures 194, 195. 



The flow through a grating of laminas or other cylinders, with a wake behind each, has 

 been considered by von Mises,^^° Betz and Petersohn,^^^ and Schmieden. ^^'^ 



Free Streamlines in a Channel 



The wake behind a body in a channel was considered in a simple case by Cisotti 

 and more generally by Villat^°''' ^^'^ and by Bergmann.^^^ A deadwater ahead of such a 

 body, or in front of the projecting bend of wall where a channel divides, was considered by 

 Agostinelli.^*^^ For a channel interrupted by openings where free streamlines occur, see 

 Colonetti,^"^ and Miyadzu.^'^*' The flow past a triangular ridge on a wall with a wake behind 

 the ridge is illustrated in Figure 196, as found by Tumlirz.^^^ 



295 



