Integral and Differential Analysis

The analysis in which large control volumes are used to obtain the aggregate forces or transfer rates is termed integral analysis. When the analysis is applied to individual points in the flow field, the resulting equations are differential equations, and the method is termed differential analysis.

2.6.2 State Equation

For air at normal temperature and pressure, the density p, pressure p and temperature T are connected by the relation p = pRT, where R is a constant called gas constant. This is known as the thermal equation of state. At high pressures and low temperatures, the above state equation breaks down. At normal pressures and temperatures, the mean distance between molecules and the potential energy arising from their attraction can be neglected. The gas behaves like a perfect gas or ideal gas in such a situation. At this stage, it is essential to understand the difference between the ideal and perfect gases. An ideal gas is frictionless and incompressible. The perfect gas has viscosity and can therefore develop shear stresses, and it is compressible according to state equation.

Real gases below critical pressure and above the critical temperature tend to obey the perfect-gas law. The perfect-gas law encompasses both Charles’ law and Boyle’s law. Charles’ law states that at constant pressure the volume of a given mass of gas varies directly as its absolute temperature. Boyle’s law (isothermal law) states that for constant temperature the density varies directly as the absolute pressure.