Basic and Subsidiary Laws

In the range of engineering interest, four basic laws must be satisfied by any continuous medium. They are:

• Conservation of matter (continuity equation).

• Newton’s second law (momentum equation).

• Conservation of energy (first law of thermodynamics).

• Increase of entropy principle (second law of thermodynamics).

In addition to these primary laws, there are numerous subsidiary laws, sometimes called constitutive relations, that apply to specific types of media or flow processes (for example, equation of state for perfect gas, Newton’s viscosity law for certain viscous fluids, isentropic and adiabatic process relations are some of the commonly used subsidiary equations in flow physics).

2.6.1 System and Control Volume

In employing the basic and subsidiary laws, any one of the following modes of application may be adopted:

• The activities of each and every given element of mass must be such that it satisfies the basic laws and the pertinent subsidiary laws.

• The activities of each and every elemental volume in space must be such that the basic laws and the pertinent subsidiary laws are satisfied.

In the first case, the laws are applied to an identified quantity of matter called the control mass system. A control mass system is an identified quantity of matter, which may change shape, position, and thermal condition, with time or space or both, but must always entail the same matter.

For the second case, a definite volume called control volume is designated in space, and the boundary of this volume is known as control surface. The amount and identity of the matter in the control volume may change with time, but the shape of the control volume is fixed, that is, the control volume may change its position in time or space or both, but its shape is always preserved.