Page 114 - Aeronautical Engineer Data Book

90 Aeronautical Engineer’s Data Book
Table 5.4 Isentropic flows

Pipe flows –dp du
= M 2
� u
Convergent Flow velocity u =
nozzle flows
k
–1

0 p
k ��
���
�
� �
ρ k
2 1 –
� � � 1k – ρ 0 p 0
Flow rate m = uA
1
�

Convergent­ � 2 � �
1/k
k– 1 p 0
divergent A
p
k + 1
Area ratio =
nozzle flow A*
�
��
�
�
k –1 �
p �
(1– k)
k + 1

p 0 k
1 –

Table 5.4 shows equations relating to conver­
gent and convergent-divergent nozzle flow.
5.6 Compressible 1D flow
Basic equations for 1D compressible flow are
Euler’s equation of motion in the steady state
along a streamline:
�
�
1 dp d 1
+ u 2 = 0
ds ds 2
or
dp 1
+ u 2 = constant
∫ 2
so:
k 1
2
RT + u = constant
k – 1 2
T 0
p 0 �� k/(k – 1) �
k – 1 2 � k/(k – 1)
= = 1 +
M
p T 2
where T = total temperature.
0