Energy balance. First principle of thermodynamics
Fluid mechanical basic equations

The first principle of thermodynamics states that the energy variation of a system in a unit of time is equal to the power of the external forces plus the thermal power exchanged between the system and its external environment (if we restrict ourselves to mechanical and thermal energy forms).

In the balance equation (3) , the quantity per unit volume g corresponds to the internal stopping energyρe _a per unit volume of the fluid. We have :