The central axis line of a well or a pipeline with a position vector \bf r at each point of trajectory given as:
| (1) | {\bf r} = {\bf r}(l) |
where
{\bf r}(l) = \{ x(l), \, y(l), \, z(l) \} | space coordinates with z-ccordinate facing down to the Earth Centre |
{\bf r}_0 | intake pipeline coordinates \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |
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 | pipeline length from inflow point \{ x_s = 0, \, y_s = 0, \, z_s = 0 \} |