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Use the rest frame of the hydrofoil, with undisturbed velocity $U_0{\mathbf{e}}_x$. Let $p_{\ast }$ be the undisturbed pressure at the lower surface level $z=0$, so the undisturbed hydrostatic pressure is $p_{\ast }-\rho gz$. The Bernoulli equation gives, with $h=a\cos (\pi x/b)$ and $ϵ=\pi a/b$,These formulas implement the prescribed neglect of the other velocity components. To the controlled first order in $a/b$, $p_{\mathrm{lower}}-p_{\mathrm{upper}}=\rho gh+\rho U_0^2ϵ\cos (\pi x/b)$. The vertical component of pressure acting on an inclined surface is integrated over its horizontal projection, soThe total upward fluid force per unit span is $L_{\mathrm{dynamic}}^{\prime }+B^{\prime }$. The lift due to motion is $L_{\mathrm{dynamic}}^{\prime }$; $B^{\prime }$ is the separate buoyancy. If the given approximate speed is squared without truncation, the formal additional dynamic term is $\rho U_0^2{\pi }^2{a}^2/(4b)$, but a controlled second-order prediction would require the omitted second-order flow and transverse-velocity contributions too.

Take positive circulation to mean counterclockwise in the $(x,z)$ diagram, with $x$ right and $z$ up. The upper surface is then traversed right to left. To first order in $a/b$,Thus the bound circulation is clockwise. Any exterior contour enclosing the hydrofoil has the same circulation in an irrotational flow; a globally completed two-dimensional flow must contain a circulation component decaying as $|\Gamma |/(2\pi r)$ at large distance. The simple local upper/lower velocity prescription cannot describe the entire exterior. For a start from rest, Kelvin's circulation theorem requires compensating shed vorticity, represented by a starting vortex in a physical wake.

Numerically,If the question's fluid force includes buoyancy, $B^{\prime }\simeq 1.25\times 10^3\mathrm{N}{\mathrm{m}}^{-1}$ and the total upward fluid force is about $2.05\times 10^3\mathrm{N}{\mathrm{m}}^{-1}$, using $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$. Weight of the hydrofoil is not specified and is not part of this fluid force. The motion-induced lift also agrees with the Kutta–Joukowski theorem, $L^{\prime }=-\rho U_0\Gamma$ in this orientation.

The chord-based Reynolds number isAt this large Reynolds number, smooth laminar flow over the whole body is unlikely in ordinary conditions; wall layers may undergo transition and separate. A thin-layer inviscid flow approximation outside them can remain useful, but does not justify globally laminar flow.