Main equations of gas transporting

The equation of motion.

Due to D`Alamber`s law the sum of all the forces affecting the molecular of oil and gas equals zero. What are these forces: the pressure, that helps to move the molecular, force of gravity, force of friction and the force of inertia.

The pressure drop is the change of the pressure of P₁ to P₂ depending on the path the molecular is made.

All the other forces impede the flow decrising the pressure drop. They are:

- inertial losses of pressure (the change of the pressure, rate and density not only in distance, but in time too);

- gravitational losses of pressure (the force required to overcome the height diference);

- hydraulic losses of pressure (the losses created by deposits in pipeline and friction of flow to the wall of the pipe).

Write the equation in differential form;

(1)

- inertial ;

- on friction ;

- gravitational .

The nature of the motion can be stationary (steady – the change of pressure, temperature and flow rate is observed only in length of pipeline) or non-stationary (unsteady – the change of above parameters in length and in time). So without the changes in time inertial losses equal zero that is why:

steady (stationary) motion

If we have deal with pipelines the difference of height between the start and end points is less than 100 metres, we can allow that we have deal with plane pipeline, with

In this case the equation of motion transfer into

steady (non-stationary) motion in planes pipeline

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