The central axis line of a well or a pipeline with a position vector
at each point of trajectory given as:| LaTeX Math Block |
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{\bf r} = {\bf r}(l) |
where
| LaTeX Math Inline |
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| body | {\bf r}(l) = \{ x(l), \, y(l), \, z(l) \} |
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| space coordinates with -ccordinate facing down to the Earth Centre |
| intake pipeline coordinates | LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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| LaTeX Math Inline |
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| body | l = \int_0^l \sqrt{dx^2 + dy^2 + dz^2} = \int_0^l \sqrt{\dot x^2 + \dot y^2 + \dot z^2} dl |
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| pipeline length from inflow point | LaTeX Math Inline |
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| body | \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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