d / 1 d[psi] \ d / 1 d[psi]\
[xi] = 0, [eta] = 0, 2[zeta] = -- ( --- ------ ) + -- ( --- ------ )
dx \ y dx / dy \ y dy /
1 /d²[psi] d²[psi] 1 d[psi]\ 1
= --- ( ------- + ------- - --- ------ ) = - ---[nabla]²[psi], (2)
y \ dx² dy² y dy / y
suppose; and in steady motion,
dH 1 d[psi] dH 1 d[psi]
-- + --- ----- [nabla]²[psi] = 0, -- + --- ------ [nabla]²[psi] = 0, (3)
dx y² dx dy y² dy
so that