Flow of Viscous Liquids. 



367 



Fig. 4. 



two independent parts by a straight partition CD 

 extending across, but perforated by an aperture 

 AB ; and that the force is applied at a distance 

 from CD on the left. If the partition were 

 complete, w and dw/dn would be zero over the 

 whole, and the displacement in the neighbour- 

 hood on the left would be simple one-dimen- 

 sional bending, with iv positive throughout. On 

 the right iv would vanish throughout. In order 

 to maintain this condition of things a certain 

 couple acts upon the plate in virtue of the 

 supposed constraints along CD. 



Along the perforated portion AB the couple 

 required to produce the one-dimensional bending 

 fails. The actual deformation accordingly differs 

 from the one-dimensional bending by the de- 

 formation that would be produced by a couple 

 over AB acting upon the plate as clamped along 

 CA, BD, but otherwise free from force. This 

 deformation is evidently symmetrical with change 

 of sign upon the two sides of CD, w being 

 positive on the left, negative on the right, and 

 vanishing on AB itself. Thus upon the whole 

 a downward force acting on the left gives rise 

 to an upward motion on the right, in opposition to the general 

 law proposed for examination. 



In the application to the hydrodynamical problem we see 

 that the fluid moving on the left from D to B passes on 

 in a straight course to A, and thence along AC, and that on 

 the right an eddy, or backwater, 

 is formed. At distances from the 

 aperture large in comparison with 

 AB the supplementary motion is 

 of the character expressed in (33'). 



A similar argument may be ap- 

 plied to the case (fig. 5) where 

 fluid moves along a wall DC into 

 which a channel AF opens, and it j 

 leads to the conclusion that the | 

 fluid on arrival at B will refuse to 

 follow the wall BF, but will rather 

 shoot across towards A. 



These examples are of some 

 interest as establishing that the 

 formation of eddies observed in 

 practice is not wholly due to 



Fig. 5. 



