173
4.8.5. We once more study the nozzle of Exercise 4.8.1. The results obtained
with the constant density formulae differ strongly from those for an ideal gas. We
analyse the origin of these differences.
The relations for constant density are:
(4.33)
The relations for ideal gas are:
(4.34)
Bernoulli :
2
2
1
1
2
2
p v
p
v .
2
2
r
r
+
=
+
Mass:
or
.
2
2
2
1
2
1
2
v D
v d
v v b
=
=
( )
Thus
and
.
2
4
1
2
2
th
4
p p
v
1
2 p
1
m
A
2
1
b
r
r
r
b
−
∆
=
−
=
−
Conservation of energy :
2
2
1
1
p 1
1
p 2
2
2
2
C T
v
C T
v
+
=
+
Thus
2
2
2
1
2
p 1
1
v
v
T
C T 1
2
2
T


−
=
−




Isentropy :
and
1
1
2
2
2
2
1
1
1
1
T
p
p
.
T
p
p
g
g
g
r
r
−
 
 
=
=
 
 
 
 
Mass:
.
2
1 1
2 2
v
v
r
r b
=
4.8 Exercises