= Solution
{c}
For the proposed <velocity field>, $u_x+w_z=1-1=0$, so <incompressibility> holds. Its <convective acceleration> is
$$
u u_x+w u_z=x,\qquad u w_x+w w_z=z,
$$
and both components have zero <Laplacian>. The <Navier-Stokes equation> therefore requires $p_x=-x$ and $p_z=-z$. Hence
$$
\boxed{p(x,z)=p_* -\frac12(x^2+z^2),}
$$
where $p_*$ is an arbitrary constant reference <pressure>. The same <pressure gradient> balances the same <convective acceleration> in the <Euler equations for an inviscid fluid>. Since the viscous terms vanish identically, this is an exact solution for every positive <Reynolds number>, as well as for the inviscid limit.
At $z=0$, the normal <velocity> is zero, and the prescribed dimensionless tangential <traction> is
$$
\boxed{\mathbf e_1\cdot\mathbf t(\mathbf e_3)=u_z+w_x=0.}
$$
This <stagnation point> flow therefore has \b[zero surface shear stress], although its <strain-rate tensor> and its viscous <normal stresses> are nonzero.
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