(1)	$\begin{array}{l}\displaystyle \frac{\partial {\bf u}}{\partial t} + ({\bf u} \cdot \nabla) {\bf u} = - \frac{1}{\rho} \nabla p +\nu \cdot \nabla^2 {\bf u} + \frac{1}{3} \cdot \nu \cdot \nabla (\nabla {\bf u}) + {\bf g} + \frac{1}{\rho}{\bf f}_{\rm cnt}\end{array}$

where

$\begin{array}{l}\rho\end{array}$	fluid density
$\begin{array}{l}\nu\end{array}$	fluid kinematic viscosity
$\begin{array}{l}{\bf g}\end{array}$	volumetric density of all body forces exerted on fluid body
$\begin{array}{l}{\bf f}_{\rm cnt}\end{array}$	volumetric density of all contact forces exerted on fluid body

In case of inviscid flow it simplifies to

Approximations

$\begin{array}{l}\mu = 0\end{array}$

$\begin{array}{l}\nabla {\bf u} =0\end{array}$

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

(3)	$\begin{array}{l}\displaystyle \frac{\partial {\bf u}}{\partial t} + ({\bf u} \cdot \nabla) {\bf u} = - \frac{1}{\rho} \, \nabla p +\nu \nabla^2 {\bf u} + {\bf g} + \frac{1}{\rho} \, {\bf f}_{\rm cnt}\end{array}$

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