8-62
8-101 Air is expanded in an adiabatic nozzle by a polytropic process. The temperature and velocity at the
exit are to be determined.
Assumptions 1 This is a steady-flow process since there is no change with time. 2 There is no heat transfer
or shaft work associated with the process. 3 Air is an ideal gas with constant specific heats.
Properties The properties of air at room temperature are cp = 1.005 kJ/kg·K and k = 1.4 (Table A-2a).
Analysis For the polytropic process of an ideal gas, Pv n
T2
§P
T1 ¨¨ 2
© P1
·
¸¸
¹
( n 1) / n
§ 200 kPa ·
(373 K)¨
¸
© 700 kPa ¹
Constant , and the exit temperature is given by
0.3 / 1.3
279 K
There is only one inlet and one exit, and thus m 1 m 2 m . We take nozzle as the system, which is a
control volume since mass crosses the boundary. The energy balance for this steady-flow system can be
expressed in the rate form as
E E
in
out
Rate of net energy transfer
by heat, work, and mass
E in
§
V2
m ¨ h1 1
¨
2
©
h1 ·
¸
¸
¹
V12
2
'E system Ê0 (steady)
0
Rate of change in internal, kinetic,
potential, etc. energies
E out
§
V2 ·
m ¨ h2 2 ¸)
¨
2 ¸¹
©
h2 +
700 kPa
100qC
30 m/s
Air
200 kPa
V 22
2
Solving for the exit velocity,
V2
>V
>V
@
0.5
2
1
2(h1 h2 )
2
1
2c p (T1 T2 )
@
0.5
ª
§ 1000 m 2 /s 2
«(30 m/s) 2 2(1.005 kJ/kg ˜ K)(373 279)K¨¨
«¬
© 1 kJ/kg
436 m/s
·º
¸»
¸»
¹¼
0.5
PROPRIETARY MATERIAL. © 2008 The McGraw-Hill Companies, Inc. Limited distribution permitted only to teachers and
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8-62 exit are to be determined.