21 



CONDITIONS IN A BOUNDARY LAYER AS RELATED TO INCEPTION OF CAVITATION 



Although some remarks have been made as to the effects of viscosity 

 on cavitation, both in a stationary fluid and as manifested in the separation 

 zone of a flowing fluid, a small point as to the effect of viscosity— in con- 

 nection with the boundary layer in the flow of real liquids over a surface 

 without separation— will be cleared up here. In the Prandtl theory of the 

 boundary layer, it is shown that the pressure change across the boundary layer 

 is a second-order effect and that the pressure at the "edge" of the boundary 

 layer is very nearly that at the solid surface, and as a matter of fact, 

 this is confirmed by experiment. However, the question has arisen from time 

 to time whether the actual pressure increases or decreases across the boundary 

 layer and, thus, whether cavitation will occur at the surface always or 

 whether it might begin just outside the boundary layer. This question is 

 especially of interest for thick boundary layers either from the standpoint 

 of the surface itself or of an appendage fixed to the surface and, thus, in- 

 side its boundary layer. The question can be answered for laminar boundary 

 layers from an examination of the Blasius solution for the laminar boundary 

 layer on a flat plate. Taking the Navier-Stokes equation for two-dimensional, 

 incompressible flow 



u |u + v |u = _l|£ + v (^fu + efu\ 

 u dx dj P ex "\ KvS ey 2/ 



dx" 



dv 



dv _ 



dx ay 



P dy v \JTx 



2" + 



8<V 

 dy 2 . 



[n] 



and the continuity equation 



dx dy 



[12] 



where u is the component of velocity in the x-direction, 

 v is the component in the y-direction, and 

 v is the kinematic viscosity, 



and using an order-of-magnitude argument, Prandtl 41 obtains the boundary layer 

 equations: 



.l*'U 



ex 



1JE-+V 



p dx 



afu 

 e y 2 



6u , dv _ n 

 dx + ey u 



[13] 



