Relation (15) holds equally well for v, ®, or p. The 

 choice of dependent variable depends largely on the nature 

 of the boundary conditions. In any event, v, ®, and p are 

 readily determined in terms of s. 



Boundary Conditions 



The dynamic and kinematic boundary conditions reqiuire 

 that continuity exist in respect to the displacement and 

 stresses at the boundaries of the system. Specifically, 

 if A denotes the difference in a given quantity across the 

 boundary of the system then it is required that 



As = 



where n^ denotes the direction cosines of the normal to 

 boundary surface. 



If the boundary is a liquid-air interface, and if both 

 fluids are considered inviscid, then it is sufficient to stipu- 

 late only 



lss n = 

 Ajj = 



(16) 



(17; 



If the air is neglected altogether, then the second condition 

 is sufficient and implies simply that p = on a truly free 

 surface. 



In the case of a thin flexible sheet separating two in- 

 viscid fluids, where the sheet can support significant tensile 

 stress, then the stress condition of (16) can be replaced by 



32 



