= Solution
{c}
Choose the <stream function> convention $u=-\psi_y$, $v=\psi_x$, so that this is an incoming <stagnation point> flow rather than the reversed flow. The <velocity field> is
$$
u=Ax,\qquad v=-Ay.
$$
At the plate $v(x,0)=0$, satisfying the <no-penetration boundary condition>. The nonzero tangential <velocity> $u(x,0)=Ax$ is permitted for an <inviscid flow>; the <no-slip boundary condition> is not imposed on the <Euler equations for an inviscid fluid>.
The steady <convective acceleration> is $(A^2x,A^2y)$. Thus the <Euler equations for an inviscid fluid> require
$$
p_x=-\rho A^2x,\qquad p_y=-\rho A^2y-\rho g.
$$
Integrating gives
$$
\boxed{p_\infty(x,y)=p_0-\frac{\rho A^2}{2}(x^2+y^2)-\rho gy.}
$$
\b[The printed formula omits $\rho$ from its quadratic term.] The source uses physical <pressure>, not <pressure> divided by <mass density>, as is clear from its $\rho gy$ term and its <Navier-Stokes equation>. The omitted factor is also required by <dimensional analysis>. For a concrete substitution check, the printed expression gives $-p_x/\rho=A^2x/\rho$ rather than the required $A^2x$ when $\rho\ne1$ in the chosen numerical units.
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