= Eulerian coordinate
{title2=$\mathbf x$}
An <Eulerian coordinate> labels a fixed spatial location at which a continuum field is evaluated. A probe fixed in a pipe records $\mathbf v(\mathbf x_0,t)$ as different fluid particles pass it. This description is convenient when the apparatus or boundary is fixed and the identities of individual particles are unimportant.
It differs from a <Lagrangian coordinate>, which labels one material particle. If the <velocity field> varies with position, that particle experiences changes both because the field evolves and because it moves into a different region. Its <material derivative> is therefore $D/Dt=\partial_t+\mathbf v\cdot\nabla$. In a steady narrowing pipe, $\partial_t\mathbf v=0$ at every <Eulerian coordinate>, yet a travelling particle can accelerate through the convective term. Steady observations do not imply zero particle <acceleration>.
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