Page 178 - 48Fundamentals of Compressible Fluid Mechanics

140 CHAPTER 9. FANNO FLOW

Furtherer rearranging equation (9.16) results in

(9.17)

in term of the Mach

number and substituting into equation (9.17). Derivative of mass conservation

(9.2) results
It is convenient to relate expressions of ( ) and
(9.18)

The derivation of the equation of state (9.6) and dividing the results by equation of

state (9.6) results

(9.19)

Derivation of the Mach identity equation (9.14) and dividing by equation (9.14)

yields

(9.20)

Dividing the energy equation (9.4) by and utilizing definition Mach number

yields

(9.21)

Equations (9.17), (9.18), (9.19), (9.20), and (9.21) need to be solved. These

This equation is obtained by
combining the definition of

Mach number with equation equations are separable so one variable is a function of only single variable (the

of state and mass conserva-
tion. Thus, the original limita- chosen independent variable). Explicit explanation is provided only two variables,
tions must be applied to the
resulting equation. , is chosen
,
rest can be done in similar fashion. The dimensionless friction,
causes the change in the other variables.

as independent variable since the change in the dimensionless resistance,
Combining equations (9.19) and (9.21) when eliminating

results
(9.22)