Basic Physical Laws

In the theory of fluid mechanics, the flow properties of fluid are generally predicted without actually measuring it. If the initial values of certain minimum number of quantities are known, then the values at some other locations can be obtained by using certain fundamental relationships. However, they are very much local in the sense that they cannot be used for different set of conditions. Such relationships are called as empirical laws/formulae and there are certain relationships which are broadly applicable in a general flow field, falling under the category of ‘basic laws'. Pertaining to the theory of fluid mechanics, there are three most relevant basic laws namely;

• •  Conservation of mass (continuity equation)

•  Conservation of momentum (Newton's second law of motion)

•  Conservation of energy (First law of thermodynamics

•  Second law of thermodynamics

All these basic laws involve thermodynamic state relations (equation of state, fluid property relation etc.) for a particular fluid being studied.

Conservation of mass : There are two ways to define mass namely, inertial mass and gravitational mass. The first one uses Newton 's second law for definition whereas the second one uses Newton 's law of gravitation. In both the cases, numerical value for mass is the same. If this numerical value does not change when the system undergoes a change, then it is treated as “conservation of mass”. In fluid flow situation, if one chooses a system of fluid particles, then the identity remains the same by definition of system and hence the mass for a system is constant. It does not matter whether any chemical reaction/heating or any other process is taking place within the system. Mathematically, it is represented as the time rate of change of mass of a system is zero.

(2.1.4)

Newton 's second law of motion : It states that the rate of change of linear momentum of a chunk of fluid mass is equal to the net external force acting on it. For a single particle, Newton 's second law is written as,

(2.1.5)

where, is the resultant force on the particle, m is the mass of the particle, is the velocity of the particle and is the acceleration of the particle. Since a fluid mass consists of number of particles, then the net linear momentum for n number of particles is given by,

(2.1.6)