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I haven't seen a clear and general definition of control volume. So if you know one, skip the context below and please give me your definition and sincerely, thank you.

Context:

The union of all the definitions is:

"A control volume is a mathematically abstract volume in space, which when observed from a inertial reference frame, is at rest or moves with uniform velocity."

  1. By the motion of the volume, I assume it to be the motion of the centroid of volume(or geometric centre) of the volume.

  2. Is the definition given correct and absolute?

  3. Would it be safe to consider an abstract volume rotating with constant angular speed to be a control volume for scientific/mathematical purposes ?

  4. An abstract volume whose geometric centre accelerates or which rotates with an increasing angular speed, it can't be referred to as control volume, can it?

Ultimately, I would like to a have a general definition of the control volume for me to follow throughout my life.

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In the most general sense, control volumes can really be defined as a totally arbitrary region of space which can move and rotate in whatever way you desire; you just have to make sure you do the accounting for all the phenomena that occur as a result (“fictitious” forces, etcetra).

However, most continuum mechanicists prefer to use control volumes that are inertial, that is, not rotating and moving with a constant velocity (which can be zero). This is so that any physical statements derived from a control volume analysis of the system are equally applicable to all other control volumes of that type, thanks to Galilean invariance.

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