\rho \left(  \frac{\partial u}{\partial t} + u \frac{\partial u}{\partial l} \right)=
-\frac{\partial p}{\partial l}  + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}

where

time

distance along the fluid flow streamline

elevation along the 1D flow trajectory 

fluid pressure

fluid density

fluid velocity vector 

fluid velocity module

standard gravity constant

volumetric density of all contact forces exerted on fluid body

projection of  onto the unit fluid velocity vector 


See also


Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid flow / Navier–Stokes equation /  Euler equation

Inviscid fluid flow ]