Fluid flow with fluid pressure $\begin{array}{l}p(t, {\bf r})\end{array}$ are not changing in time:

$\begin{array}{l}\displaystyle p(t, {\bf r}) = p({\bf r})\end{array}$

This immediately leads to the stationary fluid velocity $\begin{array}{l}{\bf u}(t, {\bf r})\end{array}$ :

(1)	$\begin{array}{l}\displaystyle {\bf u}(t, {\bf r}) = {\bf u}({\bf r})\end{array}$

Derivation

The fluid velocity is:

(2)	$\begin{array}{l}\displaystyle {\bf u}(t, {\bf r})= M({\bf r}, p, \nabla p) \nabla p\end{array}$

and

(3)	$\begin{array}{l}\displaystyle \frac{\partial {\bf u}(t, {\bf r})}{\partial t}= 0\end{array}$

which leads to (1).

The fluid temperature $\begin{array}{l}T(t, {\bf r})\end{array}$ is supposed to vary slowly enough to provide quasistatic equilibrium.

This flow regime is often observed in pipeline fluid flow and reservoir fluid flows

Page tree

See also