Page 97 - 48Fundamentals of Compressible Fluid Mechanics

4.4. ISENTROPIC ISOTHERMAL FLOW NOZZLE 59

critical adiabatic velocity by results in
(4.80)

On the other hand, the pressure loss in adiabatic flow is milder as can be seen in

Figure 4.7(a).

Isothermal Nozzle Comperison between the two models
k = 1 4 k = 1 4
4 5
4.5 M isoT
3.5
M isentropic
4
U isntropic /U isoT
3
3.5
2.5
3
2 2.5
*
1.5 A / A iso 2
*
A / A adiabatic 1.5
*
1 P / P iso
*
P / P adiabatic 1
0.5
0.5
0 0
0 0.5 1 1.5 2 2.5 3 3.5 4 0 0.5 1 1.5 2
M Distance (normalized distance two different scales)
Tue Apr 5 10:39:06 2005 Mon Jan 23 14:08:34 2006
(a) Comparison between the isothermal (b) The comparison of the adiabatic
nozzle and adiabatic nozzle in various model and isothermal model
variables
Fig. 4.7: The comparison of nozzle flow
It should be emphasis that the stagnation pressure decrees. It is conve-
nient to find expression for the ratio of the initial stagnation pressure (the stagnation
pressure before entering the nozzle) to the pressure at the throat. Utilizing equa-
tion (4.74) the following relationship can be obtained

e

(4.81)
e

Notice that the critical pressure is independent of the specific heat ratio, , as op-
pose to the adiabatic case. It also has to be emphasized that the stagnation values
e

3
'3'