Hydrodynamic Problems Solved by Rheoelectric Analogies 



r(y) = 0j - 0^ = J_ r Ap' dx' , (6) 



and xj = xj(y) is the position of the leading edge at the same section. The func- 

 tion g should be such as g(xj,y) = and g(x^,y) = -i. 



4. On the trailing edge of the wing the Kutta- Joukowski condition must be 

 respected 



30 

 Bx" 



' ^ ;: (7) 



with x^ = Xg + C as the position of the trailing edge. 



5. On the plane y = 0, by the symmetry of the flow, the normal velocity is 



y = o 

 and at infinity upstream the gradient of i also is 



grad c^ = . (9a) 



6. The cavitation pocket must be closed, i.e., in a section y = cte, on a 

 closed contour surrounding the foil and the cavity 



7. The boundary value problem defined by the conditions of Eqs. (la), (3), 

 (7) , (8) , (9a) , and (4a) or (5a) is not yet determined because the distributions of 

 the potentials on the lower and upper surface of the cavity remain arbitrary. 

 This does not, however, constitute an indetermination, for they are connected in 

 the inverse problem by the known value of Cg(y) in Eq. (5a). In the direct prob- 

 lem it may be considered as the unknown of the problem which fulfills the con- 

 dition of Eq. (7). We shall not discuss this question in detail, but rather insist 

 on the methods used for its solution. 



8. In the two-dimensional case there is an associated harmonic function 4j , 

 perturbation stream function, defined by the transformation of conditions in 

 Eqs. (la), (3), (7), (8), (9a), and (10a): 



On the free surface 



Bi/; 



F-2(0-0„) , (lb) 



o n 



on the upper and lower surface of the cavity 



373 



