Page 91 - 48Fundamentals of Compressible Fluid Mechanics

4.2. ISENTROPIC CONVERGING-DIVERGING FLOW IN CROSS SECTION 53

of referred to the theoretical minimum area (”throat area”) if the flow would con-
tinued to flow isentropic manner. Clearly, in a case where the flow isn’t isentropic or
adiabatic the total pressure and the total temperature change (due to friction, and
. Denoting subscript A

for a point and subscript B or another point mass equation (4.48) can be equated.

heat transfer). A constant flow rate requires that

(4.56)

. There

two possible models that can be used to simplify the calculations. The first model

for neglected heat transfer (adiabatic) flow and in which the total temperature re-
mained constant (Fanno flow like). The second model which there is significant
heat transfer but insignificant pressure loss (Rayleigh flow like).
From equation (4.56), it is clear that the function
If the mass flow rate is constant at any point on the tube (no mass loss
occur) then

(4.57)

For adiabatic flow, comparison of mass flow rate at point A and point B leads to

(4.58)

And utilizing the equality of
leads to

(4.59)

For a flow with a constant stagnation pressure (frictionless flow) and non adiabatic

flow reads

(4.60)

Example 4.4:

(
&
, Mach number is 2.5, and the duct
. Downstream at exit of tube, point B, the cross section

and Mach number is 1.5. Assume no mass lost and adiabatic
section area is 0.01
steady state flow, calculated the total pressure lost.
area is 0.015

At point A of the tube the pressure is
&
+