...

LaTeX Math Inline

body	p(t, {\bf r})

and are not changing in time:

LaTeX Math Block

alignment	left

p(t, {\bf r}) = p({\bf r})

This immediately leads to the stationary fluid velocity

LaTeX Math Inline

body	{\bf u}(t, {\bf r})

...

:

LaTeX Math Block

anchor	u
alignment	left

p{\bf u}(t, {\bf r}) = p{\bf u}({\bf r})

Expand

title	Derivation

Panel

borderColor	wheat
borderWidth	10

The fluid velocity is:

LaTeX Math Block

anchor	1
alignment	left

{\bf u}(t, {\bf r})

=

= M({\bf r}, p, \nabla p) \nabla p

and

LaTeX Math Block

anchor	1
alignment	left

\frac{\partial {\bf u}(t, {\bf r})}{\partial t}= 0

which leads to

LaTeX Math Block Reference

anchor	u

.

The fluid temperature

LaTeX Math Inline

body	T(t, {\bf r})

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

Versions Compared