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4.1 Basic Laws
The subscript 0 refers to the total value. The total enthalpy is constant in the nozzle:
h 0 = constant.
The combination of the work equation (4.2) and the energy equation (4.3) results in
(4.5)
As expected, we find that entropy is constant for reversible adiabatic flow ( = without heat exchange and without losses). In order to express this second constant, we
introduce the concept of total state or stagnation state. Total state refers to the state
obtained by bringing to stagnation the flow in an adiabatic, reversible way. This
state is indicated by the subscript 0.
and with the ideal gas law p = ρ RT:
With
and
/
this also results in
p
v
p
v
R c c
c c
g
= −
=
and
The process is thus polytropic with exponent γ.
For a given state p, ρ, T and v, the total state follows from
(4.6)
(4.7)
1
Tds dh
dp 0.
r
= −
=
From (4.5) follows
,
p
dp
c dT
r
=
or
.
p
p
c
dp
dp
dT
c dT RT p
p
R T
=
=
or
1
dp
dT
p ~ T
,
p
1 T
g
g
g
g
−
= −
or
and
1
1
1
T ~ T
~ T
p ~
.
g
g
g
g
r
r
r
−
−
2
p 0
p
1
c T c T
v ,
2
=
+
1
1
1
0
0
0
0
p
T
T
,
.
p
T
T
g
g
g
r
r
−
−
 
 
=
=
 
 
 
 