Momentum equation for the 1D stationary incompressible Inviscid fluid flow incompressible fluid $\begin{array}{l}\rho = \rm const\end{array}$ in Earth's Gravity with no friction it simplifies

with no contact forces (a partial case of Euler equation ):

(1)	$\begin{array}{l}\displaystyle \frac{p(l)}{\rho} + \frac{u^2}{2} - g \cdot z(l) = \rm const\end{array}$

where

$\begin{array}{l}z(l) = l \, \cos \theta\end{array}$	elevation along the 1D flow trajectory
$\begin{array}{l}l\end{array}$	measured length along the 1D flow trajectory
$\begin{array}{l}\theta(l)\end{array}$	trajectory deviation
$\begin{array}{l}u=u(l)\end{array}$	fluid velocity along the trajectory
$\begin{array}{l}p=p(l)\end{array}$	fluid pressure along the trajectory
$\begin{array}{l}\rho = \rm const\end{array}$	fluid density
$\begin{array}{l}g = \rm const\end{array}$	standard gravity constant

See Euler equation for derivation.

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See also