Page 159 - 48Fundamentals of Compressible Fluid Mechanics

8.2. DIMENSIONLESS REPRESENTATION 121

(8.6)

It is convenient to define a hydraulic diameter

Cross Section Area
(8.7)
wetted perimeter

2
Now, the Fanning friction factor is introduced, this factor is a dimensionless friction
#
factor sometimes referred to as the friction coefficient as following:
(8.8)
' )
Substituting equation (8.8) into momentum equation (8.2) yields

(8.9)

yield:
Rearranging equation (8.9) and utilizing the identify for perfect gas

(8.10)

as a function of the Mach number have to substitute along

with velocity, .

Meta
Now the pressure,
hould this material presented?

(8.11)
Differentiation of equation (8.11) yields

(8.12)

(8.13)

for isothermal process and therefore

Now it can be noticed that
(8.14)

2 It should be noted that Fanning factor based on hydraulic radius, instead of Diameter friction equa-

tion, thus ”Fanning f” values are only 1/4th of ”Darcy f” values.