| (1) | \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
\theta(l) | inclinational deviation, \displaystyle \cos \theta = dz/dl |
z(l) | elevation along the 1D flow trajectory |
p | fluid pressure |
\rho | fluid density |
{\bf u} | fluid velocity |
g | standard gravity constant |
{\bf f}_{\rm cnt} | volumetric density of all contact forces exerted on fluid body |
See also
Physics / Mechanics / Continuum mechanics / Fluid Mechanics / Fluid Dynamics / Fluid flow / Navier–Stokes equation / Euler equation