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Mechanical equilibrium of fluids

This equation places a restriction on the body forces. Mechanical equilibrium can exist only if the body force field satisfies…

The balance of entropy

The entropy is a thermodynamic variable of state; an extensive quantity. It cannot be experienced directly; as a derived variable…

The principle of conservation of energy

Any material system is characterized by its energy content. Energy occupies a position of distinction amongst the other extensive variables.…

The balance of kinetic energy

Let Ek denote the kinetic energy of a material volume: Although the kinetic energy is an extensive variable it is not a…

The balance of angular momentum

The principle of conservation of angular momentum belongs to the axioms of mechanics. In spite of its general validity it…

The balance of momentum

Newton’s second law of motion is perhaps the most important statement in the field of dynamics. As is well-known this states that…

The principle of conservation of mass

The transport theorem

The material derivative of a volume integral over a volume of flowing fluid

Relationships between the acceleration- and the vorticity fields

Important relationships can be obtained for the fluid flow by examining some of the obvious identities relating to the acceleration,…

Rotational motion, vorticity field

In order to illustrate this concept, we consider a typical fluid element of certain volume at any arbitrary time as…

Motion of an infinitesimal fluid particle

Imagine an infinitesimal rectangular fluid particle of fixed identity in a flowing fluid. Its sides dx, dy and dz are parallel to…

The acceleration field

The acceleration is the rate of change of the velocity experienced by a moving particle. It can be expressed as…