= Solution
Use the <rest frame> of the <hydrofoil>, with undisturbed velocity $U_0\mathbf e_x$. Let $p_*$ be the undisturbed <pressure> at the lower surface level $z=0$, so the undisturbed <hydrostatic pressure> is $p_*-\rho gz$. The <Bernoulli equation> gives, with $h=a\cos(\pi x/b)$ and $\epsilon=\pi a/b$,
$$
\boxed{p_{\rm lower}=p_*,\qquad
p_{\rm upper}=p_*-\rho gh+
\frac{\rho U_0^2}{2}\left[1-\{1+\epsilon\cos(\pi x/b)\}^2\right].}
$$
These formulas implement the prescribed neglect of the other velocity components. To the controlled first order in $a/b$, $p_{\rm lower}-p_{\rm upper}=\rho gh+\rho U_0^2\epsilon\cos(\pi x/b)$. The vertical component of <pressure> acting on an inclined surface is integrated over its horizontal projection, so
$$
\boxed{L'_{\rm dynamic}=2\rho U_0^2a,\qquad
B'=\rho g\int_{-b/2}^{b/2}h\,dx=\frac{2\rho gab}{\pi}.}
$$
The total upward fluid <force> per unit span is $L'_{\rm dynamic}+B'$. The <lift> due to motion is $L'_{\rm dynamic}$; $B'$ is the separate <buoyancy>. If the given approximate speed is squared without truncation, the formal additional dynamic term is $\rho U_0^2\pi^2a^2/(4b)$, but a controlled second-order prediction would require the omitted second-order flow and transverse-velocity contributions too.
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