Solution
= Solution
For steady inviscid flow, Bernoulli's equation along a <streamline> is
$$
p+\frac12\rho|u|^2+\chi=\text{constant}.
$$
Writing steady Euler flow in divergence form and integrating over $V$ gives
$$
\int_{\partial V}(\rho(u\cdot n)u+pn+\chi n)\,dS=0
$$
by incompressibility and the divergence theorem.