Page 181 - 48Fundamentals of Compressible Fluid Mechanics

9.4. THE WORKING EQUATIONS 143

9.3.0.2 The Trends
The trends or whether the variables are increasing or decreasing can be observed
from looking at the equation developed. For example, the pressure can be exam-
ined by looking at equation (9.26). It demonstrates that the Mach number increases
downstream when the flow is subsonic. On the other hand, when the flow is super-
sonic, the pressure decreases.
The summary of the properties changes on the sides of the branch

This table is only for a histor-
ical reason, is there another
Subsonic Supersonic way to represent this informa-
tion?
decrease increase
increase decrease
increase decrease
Pressure,
Mach number,
decrease increase
Density, decrease increase
Velocity,
decrease increase
Temperature,
Stagnation Temperature,
9.4 The working equations
Integration of equation (9.25) yields

(9.36)

%

A representative friction factor is defined as %

(9.37)

Utilizing the mean average theorem equation (9.36) yields

(9.38)
"

%

It common to replace the with
which is adopted in this book.
%

Equations (9.24), (9.27), (9.28), (9.29), (9.29), and (9.30) can be solved.
"
, and

and describe the pres-
For example, the pressure as written in equation 9.23 is represented by
sure on the Mach number. Dividing equation 9.24 in equation 9.26 yields

Mach number. Now equation 9.24 can eliminate term
(9.39)

%