Modern Engineering Thermodynamics

16.6 Choked Flow 667
Exercises
16. Determine the fill-tube diameter in Example 16.7 for a compressed air storage (stagnation) pressure of 3000. psia.
Assume all the other variables remain unchanged. Answer: D tube = 0.890 in.
17. Suppose the air bag in Example 16.7 is filled with helium instead of air. Determine the minimum fill-tube diameter
required, assuming all the other variables remain unchanged. Answer: D tube = 0.787 in.
18. Determine the air bag minimum fill-tube diameter in Example 16.7 if the variables are changed to D bag = 1.0 m,
T os = 20.0°C, p os = 10.0 MPa, and p bag = 0.103 MPa. Answer: D tube = 0.0370 m.
When M throat = 1:0, the nozzle is passing its maximum flow rate and no changes made downstream of the throat
(such as lowering the exit pressure) will cause the flow to increase. Consequently, the nozzle is said to be choked
when the velocity of the fluid at its throat reaches sonic velocity.
Dividing Eq. (16.22a) by (16.21) gives the nozzle to throat cross-sectional area ratio for a supersonic nozzle at
its maximum flow rate, and for air ðk = 1:4Þ, this becomes
for air (k = 1.40), this becomes
A/A = 1 M
2
k + 1
1 + k−1 ðk+1Þ/2ðk−1Þ
2 M2
(16.23a)
The ratio of the nozzle air flow cross-sectional area (A), where the Mach number is M,
to the throat cross-sectional area (A*), where the mach number is M throat = 1.0 is:
ðA/A Þ air = 1 1 + 0:2M 2
M 1:2
(16.23b)
3
HOW DO AUTOMOBILE AIR BAGS WORK?
Why are air bags inflated with a chemical reaction rather than with compressed air? (See Example 16.7 for the answer.)
Air bags are widely used in automobiles to protect occupants in the event of collision. It is essential that the bag inflate
within a few milliseconds. Therefore, the gas must be nontoxic and nonflammable and be produced by a very rapid
chemical reaction.
Most air bags contain a mixture of solid sodium azide, NaN 3 , and iron oxide, Fe 2 O 3 , as the source of inflating gas because
sodium azide contains 65% nitrogen (by mass) and it decomposes very rapidly at temperatures of 350ºC or higher:
and
2NaN 3 ! 2NaðlÞ + 3N 2 ðgÞ
6NaðlÞ + Fe 3 O 2 ! 3Na 2 OðsÞ + 2FeðsÞ
Because sodium azide is poisonous, all the products and reactants are kept in a sealed container with only the nitrogen gas
being allowed to enter the “air” bag.
The decomposition is initiated about 10 milliseconds into a crash by a fuse wire activated by a collision sensor. The
bag is completely filled within 30 milliseconds, and porous sections of the bag allow it to deflate in 100 to
200 milliseconds.
CRITICAL THINKING
The term choked implies an asphyxiating, suffocating, clogged, or otherwise impeded condition. How would you explain the
concept of choked flow as used in compressible fluid flow in nontechnical language to a liberal arts friend?