161
4.4 Shape of a Nozzle
the Mach number cannot exceed the value 1 at any place. Assuming that this would
occur somewhere, the sketch in Fig. 4.3 at the right bottom demonstrates that the
Mach number would decrease immediately. So, M = 1 can maximally be attained in
the outlet section of the channel. The pressure in the outlet section, corresponding to
M = 1 is termed the critical pressure ( p * ). The corresponding state is called critical
state. The relevant state parameters follow from (4.15) for M = 1, being
(4.19)
For g = 1.4 the corresponding numerical values are
1
1
1
*
*
*
0
0
0
T
p
2
2
2
,
,
.
T
1
1
p
1
g
g
g
r
g
r
g
g
−
−
=
=
=
+
+
+
*
*
*
0
0
0
T
p
0.833 ,
0.634 ,
0.528.
T
p
r
r
=
=
=
Fig. 4.3 Expansion and
compression in subsonic and
supersonic flow
Fig. 4.4 Pressure evolution in a convergent and convergent-divergent nozzle
4.4 Shape of a Nozzle
the Mach number cannot exceed the value 1 at any place. Assuming that this would
occur somewhere, the sketch in Fig. 4.3 at the right bottom demonstrates that the
Mach number would decrease immediately. So, M = 1 can maximally be attained in
the outlet section of the channel. The pressure in the outlet section, corresponding to
M = 1 is termed the critical pressure ( p * ). The corresponding state is called critical
state. The relevant state parameters follow from (4.15) for M = 1, being
(4.19)
For g = 1.4 the corresponding numerical values are
1
1
1
*
*
*
0
0
0
T
p
2
2
2
,
,
.
T
1
1
p
1
g
g
g
r
g
r
g
g
−
−
=
=
=
+
+
+
*
*
*
0
0
0
T
p
0.833 ,
0.634 ,
0.528.
T
p
r
r
=
=
=
Fig. 4.3 Expansion and
compression in subsonic and
supersonic flow
Fig. 4.4 Pressure evolution in a convergent and convergent-divergent nozzle