165
4.6 Nozzle with Losses: Infinitesimal Efficiency
(4.21)
From η ∞ n(  γ-1) = γ(  n-1) it follows
The denominator exceeds 1, since γ > 1, so follows: n < γ.
Examples: γ = 1.4, η ∞ = 0.9: n = 1.346; γ = 1.3, η ∞ = 0.9: n = 1.262.
The endpoint of the expansion (1 in Fig. 4.5, left) may be determined from the
isentropic efficiency. The polytropic exponent and the infinitesimal or polytropic
efficiency follow from this. The polytropic efficiency does not exactly equal the
isentropic efficiency, which is slightly higher. This effect is termed reheat effect. We
discuss it in the next section.
Taking the initial velocity into account, we obtain
(4.22)
(4.23)
So (4.22) x (4.23) gives
The factor C is very close to 1.
Thus:
.
n
n 1
1
g
h
g
∞
=
−
−
n
.
(
1)
( 1
)
g
g
g h g
h
h g
∞
∞
∞
=
=
−
−
+ −
and
.
2
2
2
0
0
00
00
v
v
h h
h h
2
+ =
+ =
1
0
0
Polytropic:
.
n
n
h
p
h
p
−
 
=  
 
1
Isentropic:
.
0
0
00
00
h
p
h
p
g
g
−


= 



1
n 1
n 1
1 n 1
n 1
n 1
n
n
n
n
n
0
00
0
00
00
00
0
00
00
00
p
p
p
p
p
p
h
C
,
h
p
p
p
p
p
p
g
g
g
g
−
−
−
−
−
−
−
−
















=
=
=






























and
.
p
00
00
p 00
00
00
c
p
h
c T
RT
R
1
g
g
r
=
=
= −
and
n 1
1
1 (
)/ (
)
1
1
n
2
0
0
0
00
0
00
00
00
0
h
h
T
T
1
C
1
M .
h
h
T
T
2
g
h
h
g
g
∞
∞
−
−
−
−
−






−
=
=
=
= +











