Desai and Lieber 



2. There is slipping at a solid boundary and this slipping is resisted by a 

 force proportional to the relative velocity. 



3. A very thin layer of fluid remains completely attached to the walls and 

 the rest of the fluid slips over it. If the walls are of the same material every- 

 where, the layer has a constant thickness, so that its surface presents to the 

 current the same irregularities as those of the wall itself. The thickness of the 

 layer is different for different liquids or different materials of the wall; and it 

 depends on the curvature of the wall and on the temperature. Further, it is zero 

 for liquids which do not wet the wall. 



The above hypotheses are essentially quoted from volume n, pages 676-677 

 of Ref. 13. 



Serious objections can be raised against the third hypothesis. It includes 

 two assumptions about the thickness of the fluid layer which contradict each 

 other. The first asserts that if the walls are of the same material everywhere, 

 the layer has a constant thickness, so that its surface presents to the current 

 the same irregularities as those of the wall itself. The second asserts that the 

 thickness depends on the curvature of the wall. 



To see how the above two assumptions involve a contradiction, let us sup- 

 pose that we have a wall of the same material and that it has irregularities so 

 that its cross section is as shown in Fig. B. Suppose A to be the maximum 

 depth within which the surface irregularities are confined and that A is small 

 enough compared to a representative dimension of the wall so that the surface 

 variations within this depth can be considered as irregularities. Let us now 

 construct a curve at a depth A/ 2 such that part of the surface variations fall 

 above it and part of them fall below it. This would be a continuous curve drawn 

 along the centerline C/L shown in Fig. B. We draw it separately in Fig. C. 



Fig. B - Cross section of a wall 

 with irregularities 



Fig. C - Curve with surface variations 

 partly above and partly below A 



504 



