Page 212 - 48Fundamentals of Compressible Fluid Mechanics

174 CHAPTER 10. RAYLEIGH FLOW

constant Pressure line

Fig. 10.2: The Temperature entropy diagram for Rayleigh line

results in

(10.14)

Combining equations (10.12) and (10.13) by eliminating

E

On T-s diagram a family of curve can be drawn for a given constant. Yet for every

$'&)( (
E
curve several observations can be generalized. The derivative is equal to zero
!"
#
or when . The derivative is equal to infinity,
+*-, *

to put a mathematical expla- when . From thermodynamics, increase of heating results in

nation how the curves are when E
constructed. increase of entropy. And cooling results in reduction of entropy. Hence, when

cooling applied to a tube the velocity decreases and heating applied the velocity

or
increases. The peculiars point of when additional heat is applied the

, yet note this
point is not the choking point. The chocking is occurred only when because

it violate the second law. The transition to supper sonic flow occurs when the area

changes, some what similarly to Fanno flow, Yet, chocking can be explained by the

temperature is decreasing. The derivative is negative,
fact increase of energy must accompanied by increase of entropy. But the entropy
of supersonic flow is lower (see the Figure 10.2) and therefore it is not possible
(the maximum entropy at .).
It is convent to referrers to the value of . These value referred as the