Problem 13.31
[Difficulty: 3]
Given:
Temperature and pressure in a tank; nozzle with specific area
Find:
Mass flow rate of gas; maximum possible flow rate
Solution:
The given or available data is:
R
=
296.8
J/kg.K
k
=
1.4
T
0
=
450
K
p
0
=
150
kPa
A
t
=
30
cm
2
A
t
=
0.003
m
2
p
b
=
100
kPa
Equations and Computations:
Assuming that the nozzle exit pressure is the back pressure:
p
e
=
100
kPa
Then the nozzle exit Mach number is:
M
e
=
0.7837
This nozzle is not choked. The exit temperature is:
T
e
=
400.78
K
From
T
e
and Eq. 12.18
(12.18)
c
e
=
408.08
m/s
Then
V
e
=
319.80
m/s
From the ideal gas equation of state, we can calculate the density:
e
=
0.8407
kg/m
3
Therefore the mass flow rate is:
m
=
0.807
kg/s
When the room pressure can be lowered, we can choke the nozzle.

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