Page 162 - 48Fundamentals of Compressible Fluid Mechanics

124 CHAPTER 8. ISOTHERMAL FLOW

. Heat transfer have a limited
value therefore model of the flow must be changed. A more appropriate model is
(
) has a finite value which means that
an adiabatic flow model.

Integration of equation (8.27) yields
(8.28)

.
Using definition for perfect gas of
Denote the supper script of symbol for the above condition and one can obtain
and noticing that

that

can be used to describe the relation of the properties at

(8.29)

Rearranging equation (8.29) transfered into

(8.30)

Utilizing the continuity equation provides

(8.31)

Reusing the perfect–gas relationship

(8.32)

Now utilizing the relation for stagnated isotropic pressure one can obtain

(8.33)

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Substituting for
equation (8.32 ) and rearranging yields

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(8.34)

And the stagnation temperature at the critical point can be expressed as

(8.35)

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These equations (8.30)-(8.35) are represented on in Figure 8.2

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