Page 80 - 48Fundamentals of Compressible Fluid Mechanics

42 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW
Static Properties As A Function of Mach Number

1

0.9

0.8 P/P
0
r/r
0.7 0
T/T
0
0.6
0.5
0.4

0.3

0.2
0.1

0
0 1 2 3 4 5 6 7 8 9
Mach number
Mon Jun 5 17:39:34 2006

Relationships for Small Mach Number
4.1.2 Fig. 4.3: The stagnation properties as a function of the Mach number,
Even with today computers a simplified method can reduce the tedious work in-
volve in computational work. In particular, the trends can be examined with an-
alytical methods. It further will be used in the book to examine trends in derived
models. It can be noticed that the Mach number involved in the above equations
is in a square power. Hence, if an acceptable error is of about one percent than

provides the desire range. Further, if higher power is used, much smaller
error results. First it can be noticed that the ratio of temperature to stagnation

temperature, is provided in power series. Expanding the equations results ac-
cording to binomial expansion to

(4.16)

In the same fashion

(4.17)

%
%