The basic relations for an infinite steady flow around a thin hydrofoil with a jet flap are obtained as the solution of the Riemann-Hilbert-Poincare problem, and the first and second-order problem at small incidence and small deflection angle of the jet is analytically solved by means of the matched asymptotic expansions in the case of the jet-momentum coefficient small. Expressions for lift, drag, pitching-moment, and the cavity shape have been obtained as the asymptotic expansions in powers of the jet-momentum coefficient together with its logarithm. From the comparison of the lift with numerical results of Ho, the analytical method in this paper is seen to be very useful and reasonable.

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