Page 94 - 48Fundamentals of Compressible Fluid Mechanics

56 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

gas model is again assumed (later more complex models can be assumed and
constructed in a future versions). In isothermal process the perfect gas model
reads
(4.61)

5
Substituting equation (4.61) into the momentum equation yields

(4.62)
Integration of equation (4.62) yields the Bernoulli’s equation for ideal gas in isother-

mal process which reads

(4.63)

Thus, The velocity at point 2 becomes

(4.64)
,

reads

The velocity at point 2 for stagnation point,
(4.65)
,

Or in explicit terms of the stagnation properties the velocity is

(4.66)
,

Transform from equation (4.63) to a dimensionless form becomes

(4.67)

Simplifying equation (4.67) yields

(4.68)

Or in terms of the pressure ratio equation (4.68) reads

(4.69)

5 1 1 "

which are neglected here. 1 other effects
The one dimensional momentum equation for steady state is