Page 177 - 48Fundamentals of Compressible Fluid Mechanics

9.2. MODEL 139

It is convenient to substitute but it is referred to the same hydraulic
diameter. The infinitesimal area that shear stress is acting on is
for of
(9.9)

Introducing the Fanning friction factor as a dimensionless friction factor which

)
some times referred to as friction coefficient and reads as following:

(9.10)
' )
Utilizing equation (9.2) and substituting equation (9.10) into momentum equation

(9.6) yields

(9.11)

Dividing equation (9.11) by the cross section area, and rearranging

yields
(9.12)

The second law is the last equation to be utilized to determine only the flow direc-

tion.
(9.13)

9.2.1 Dimensionalization of the equations
Before solving the above equation a dimensionless process is applied. Utilizing
the definition of the sound speed to produce the following identities for perfect gas
(9.14)

%

Utilizing the definition of the ideal gas results

(9.15)

Utilizing the identify in equation (9.14) and substituting it into equation (9.11) and

after some rearrangement yields %

(9.16)