; ,.--'m '•'-•' -• Malavard 



2. Inside the cavity where p = p the equilibrium of its boundary requires 



that 



^-^^ F-(z„-z) , (2a) 



Bx 2 



which becomes after integration 



s 

 4>' = ^o(y) +T'' + f"' J (Zq-z) d^ , (3) 



where ^g is the value of the perturbation velocity potential at point ^o? zo> 

 (for example, the velocity potential of the leading edge), and where the signs + 

 and - relate to the upper and lower surface of the cavity. The cavitation number 

 cr is defined as 



PO - Pc . • •:■ . 



cr ~ 



(pVof/2) 



3. On the lower surface of the hydrofoil the boundary condition can be given 

 in two ways: •,. • 



A. Direct problem. The geometric form of the wing f -(x,y) is given, 

 then the velocity tangential condition permits us to write 



!^ = lil , r ' ' ■" (4a) 



3 z dx ;■ 



which is the classical Neumann condition. 



B. Inverse problem. The pressure distribution over any local chord 

 Ap' = p - p^ is given. The boundary condition may be written 



3x ^ ^ (pVoV2) ^ ^ P 



This equation can be integrated to obtain a Dirichlet condition 



0" - 0j(y) + f C,(y) g(x-xj,y) + ^x + F-2 r (Zo-z)d^, (5a) 



where C6(y) = 2r{y)/N^C{y) is the local lift coefficient at a given section y = cte 

 with chord C(y),r (y) is the circulation around this section, 



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