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This immediately leads to the stationary fluid velocity 

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

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The In the most general case (both reservoir and pipelines) the fluid velocity is proportional to pressure gradient and can be written as:

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

and which is not dependent on time in stationary:

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

which leads to

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