Page 105 - 48Fundamentals of Compressible Fluid Mechanics

4.7. THE EFFECTS OF REAL GASES 67

can be expressed in equation (3.19). Differentiating equation (3.19) and dividing
by equation (3.19) yields

(4.101)

Again, Gibb’s equation (4.27) is reused to related the entropy change to the

. The enthalpy is a function of the

and full differential is
change in thermodynamics properties and applied on non-ideal gas. Since

and utilizing the equation of the state

(4.102)
temperature and pressure thus,

The definition of pressure specific heat is and second derivative is

Maxwell relation hence,

(4.103)

First, the differential of enthalpy is calculated for real gas equation of state as

(4.104)

Equations (4.27) and (3.19) are combined to form

(4.105)

The mechanical energy equation can be expressed as

(4.106)

At the stagnation the definition requires that the velocity is zero. To carry the

integration of the right hand side the relationship between the pressure and the
density has to be defined. The following power relationship is assumed
(4.107)

Notice, that for perfect gas the is substituted by . With integration of equation

(4.106) when using relationship which is defined in equation (4.107) results
(4.108)