What is a control volume in continuum mechanics?

In continuum mechanics and thermodynamics, a control volume is a mathematical abstraction used to model physical processes. It defines a fictitious region fixed in space or moving with constant flow velocity, enclosed by a closed surface known as the control surface. At steady state, the mass entering this arbitrary region equals the mass leaving it, while fluid mechanics itself models matter from a macroscopic viewpoint without using atoms.

What we know

• A control volume is a mathematical abstraction employed in creating mathematical models of physical processes in continuum mechanics and thermodynamics. [2]
• It consists of a fictitious region of a given volume fixed in space or moving with constant flow velocity through which a continuous medium flows. [2]
• The closed surface enclosing the control volume region is referred to as the control surface. [2]
• Fluid mechanics is a branch of continuum mechanics that models matter from a macroscopic viewpoint rather than from a microscopic one using atoms. [3]

Where to go next

• the bigger pictureHow does fluid mechanics model matter without using atoms?
• compared withWhat is a free body diagram in classical mechanics?
• how it workedHow does the Cauchy stress tensor define the state of stress inside a material?
• a case in pointWhat is strain in mechanics?
• what followedHow do conservation laws apply to continuous media?
• an unexpected connectionHow does a mathematical abstraction for fluids relate to solid body deformations?Although control volumes are heavily associated with fluid flows and thermodynamics, they share fundamental continuum mechanics foundations with solid deformation theories like strain and the Cauchy stress tensor.

Sources

• [1]control volume (Wikidata Q5165895) · CC0 1.0
• [2]Control volume · CC BY-SA 4.0
• [3]Fluid mechanics · CC BY-SA 4.0
• [4]Strain (mechanics) · CC BY-SA 4.0
• [5]Cauchy stress tensor · CC BY-SA 4.0