Momentum equation for Inviscid fluid flow (a partial case of Navier–Stokes equation):

\frac{\partial {\bf u}}{\partial t} + ({\bf u} \cdot \nabla) {\bf u} =
- \frac{1}{\rho} \, \nabla p + {\bf g} +\frac{1}{\rho} \cdot {\bf f}_{\rm cnt}

where

	fluid velocity
	fluid density
	fluid kinematic viscosity
	resulting specific body force exerted on fluid body
	volumetric density of all contact forces exerted on fluid body

Approximations

Transient 1D Inviscid fluid flow

\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}

Steady-state 1D inviscid fluid flow

\frac{d p}{d l} =
-\rho \, u \, \frac{d u}{d l}  + \rho \, g \, \cos \theta + f_{\rm cnt, \, l}

Bernoulli equation =
Steady-state 1D inviscid fluid flow of incompressible fluid with no friction

\frac{p(l)}{\rho} +  \frac{u^2}{2} -  g \cdot z(l)   = \rm const

Approximations

See also