Page 90 - 48Fundamentals of Compressible Fluid Mechanics

52 CHAPTER 4. ISENTROPIC VARIABLE AREA FLOW

The equation (4.49), relates the Mach number at specific point at the duct to the
cross section area.
The maximum flow rate can be expressed either by taking the derivative of
equation (4.49) in with respect to M and equating to zero. Carrying this calculation
results at
.

(4.50)

For specific heat ratio,
(4.51)
,

"

3'%

) becomes,

(/
The maximum flow rate for air ( %!(

(4.52)
"

Equation (4.52) is known as Fliegner’s Formula on the name of one of the first

engineer who observed experimentally the choking phenomenon.
It can be noticed that Fliengner’s equation is actually dimensionless equa-

%
tion and lead to definition of the Fliengener’s Number.

(4.53)

If the Fliengner’s number as above at the every point it will be

2

(4.54)

and the maximum point point

(4.55)

4.2.3.1 Flow with pressure losses
The expression for the mass flow rate (4.47) is appropriate regardless the flow is
isentropic or adiabatic. That expression was derived based on the theoretical total
pressure and temperature (Mach number) which does not based on the considera-
tions whether the flow is isentropic or adiabatic. In the same manner the definition