Bernoulli

In many quasi-stationary applications with negligible viscous forces, one can use the Bernoulli equation to give an analytical estimate of the flow results (or parts of it). Bernoulli states

\begin{align} p_0 + \frac{1}{2}\rho {\bf v}^T{\bf v} + \rho{\bf g}^T{\bf x} = \text{const} \end{align}

It is valid throughout the flow domain (in this case we have potential flow, i.e. flow with no rotation) - at least, it is valid for each pathline of the flow.