Governing Equations in Relative and Absolute Frames

In this section the governing equations employed in the different impeller model implementations are presented. 

The fictitious forces are conventionally derived with the help of the framework of classical mechanics of a point particle. Newtonian mechanics recognizes a special class of coordinate systems called inertial frames. The Newton s laws of motion are defined in such a frame. A Newtonian frame (sometimes also referred to as a fixed, absolute or absolute frame) is undergoing no accelerations and conventionally constitute a coordinate system at rest with respect to the fixed stars or any coordinate system moving with constant velocity and without rotation relative to the inertial frame. The latter concept is known as the principle of Galilean relativity. Speaking about a rotating frame of reference we refer to a coordinate system that is rotating relative to an inertial frame. 

The Laboratory framework is frequently assumed to be inertial and adequate for practical engineering problems on the earth although the laboratory framework is actually fixed to a rotating planet and is therefore strictly speaking an accelerated frame (i.e., this approximation is not valid for large scale ocean and atmospheric flows). To describe the fluid flow caused by the impeller motion in stirred tanks both rotating and laboratory frames have been employed. 

For completeness it is mentioned that the transformations between different sets of coordinates describing the same motion, characterize a branch of classical mechanics named kinematics which is fundamentally mathematical methods, and is not based on physical principles. 

1 Governing Enlerian Flow Equations in the Laboratory Frame 

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