= Solution
For a steady inviscid incompressible fluid of constant density in uniform gravity $\mathbf g=-g\mathbf e_z$, the <Euler equation for fluid motion> and continuity equation are
$$
\rho(\mathbf u\cdot\nabla)\mathbf u=-\nabla p+\rho\mathbf g,\qquad \nabla\cdot\mathbf u=0.
$$
Taking the scalar product with $\mathbf u$ gives
$$
(\mathbf u\cdot\nabla)\left(\frac12|\mathbf u|^2+\frac p\rho+gz\right)=0.
$$
Thus \b[Bernoulli's quantity is constant along each streamline]. For an irrotational connected flow it is constant throughout the flow; constancy across different <streamlines> is not assumed in general.
Since incompressibility makes $\nabla\cdot(\rho\mathbf u\otimes\mathbf u)=\rho(\mathbf u\cdot\nabla)\mathbf u$, integrating over a fixed control volume and applying the <divergence theorem> yields the integral momentum balance
$$
\boxed{\int_S\rho\mathbf u(\mathbf u\cdot\mathbf n)\,dS
=-\int_Sp\mathbf n\,dS+\int_V\rho\mathbf g\,dV.}
$$
Here $\mathbf n$ is outward and the left side is the net outgoing <momentum flux>. Uniform atmospheric <pressure> has zero resultant on a closed control surface, so it may be subtracted from all pressures in the jet calculations.
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