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@wikipedia
Fluid flow with fluid pressure
p(t, {\bf r}) is not changing in time:
|
p(t, {\bf r}) = p({\bf r}) |
This immediately leads to stationary fluid velocity
{\bf u}(t, {\bf r}) :
(1) |
{\bf u}(t, {\bf r}) = {\bf u}({\bf r}) |
Derivation
In the most general case (both reservoir and pipelines) the fluid velocity is proportional to pressure gradient and can be written as:
(2) |
{\bf u}(t, {\bf r})= M({\bf r}, p, \nabla p) \nabla p |
which is not dependent on time in stationary:
(3) |
\frac{\partial {\bf u}(t, {\bf r})}{\partial t}= 0 |
which leads to
(1).
The fluid temperature
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
See also
Physics / Fluid Dynamics
[ Steady State Well Flow Regime (SS) ]