(1)	$\begin{array}{l}\displaystyle \rho \left( \frac{\partial {\bf u}}{\partial t} + ({\bf u} \cdot \nabla) {\bf u} \right)= -\nabla p + \rho \, {\bf g} + {\bf f}_{\rm cnt}\end{array}$

Approximations

1D non-stationary fluid flow (for example along a pipeline trajectory) takes form:

(2)	$\begin{array}{l}\displaystyle \rho \left( \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial l} \right)= -\frac{\partial p}{\partial l} + \rho \, g_l + f_{\rm cnt, \, l}\end{array}$

1D stationary fluid flow (for example along a pipeline trajectory) takes form:

(3)	$\begin{array}{l}\displaystyle \frac{d p}{d l} = -\rho \, u \, \frac{\partial u}{\partial l} + \rho \, g_l + f_{\rm cnt, \, l}\end{array}$

which is a guiding equation in pipe flow simulations

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