Page 95 - 48Fundamentals of Compressible Fluid Mechanics

4.4. ISENTROPIC ISOTHERMAL FLOW NOZZLE 57

) in the isothermal flow the stag-
nation temperature ratio can be expressed

As oppose to the adiabatic case (

(4.70)

%
%

Utilizing conservation of the mass %
to yield
%

(4.71)

Combing equation (4.71) and equation (4.69) yields

e
(4.72)

e

The change in the stagnation pressure can be expressed as

"
e

(4.73)

e

%

The critical point, at this stage, is unknown (at what Mach number the nozzle is

%

choked is unknown) so there are two possibilities: the choking point or
to

"
&
(
so results can be compared to the adiabatic case and denoted by star. Again it
has to emphasis that this critical point is not really related to physical critical point
normalize the equation. Here the critical point defined as the point where
but it is arbitrary definition. The true critical point is when flow is choked and the
relationship between two will be presented.
The critical pressure ratio can be obtained from (4.69) to read
(4.74)

e

Equation (4.72) is reduced to obtained the critical area ratio writes

(4.75)

e
Similarly the stagnation temperature reads

(4.76)

%
Finally, the critical stagnation pressure reads

(4.77)

%
1