Stationary Fluid flow with fluid staying at quasistatic equilibrium and fluid pressure and temperature are with fluid pressure

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body	p(t, {\bf r})

is not changing in time:

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anchor	p
alignment	left

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

This immediately leads to stationary fluid velocity

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

:

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anchor	u
alignment	left

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

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title	Derivation

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borderWidth	10

In the most general case (both reservoir and pipelines) the fluid velocity is a function of pressure and pressure gradient and can be written as:

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anchor	1
alignment	left

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

with right side not dependent on time in stationary flow:

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T

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

which leads to

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anchor	u

.

The fluid temperature

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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.

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