EXAMPLE 5–4 Deceleration of Air in a Diffuser

Air at 10°C and 80 kPa enters the diffuser of a jet engine steadily with a

velocity of 200 m/s. The inlet area of the diffuser is 0.4 m^2. The air leaves

the diffuser with a velocity that is very small compared with the inlet veloc-

ity. Determine (a) the mass flow rate of the air and (b) the temperature of

the air leaving the diffuser.

Solution Air enters the diffuser of a jet engine steadily at a specified veloc-

ity. The mass flow rate of air and the temperature at the diffuser exit are to

be determined.

Assumptions 1 This is a steady-flow process since there is no change with

time at any point and thus mCV0 and ECV0. 2 Air is an ideal gas

since it is at a high temperature and low pressure relative to its critical-point

values. 3 The potential energy change is zero, pe 0. 4 Heat transfer is

negligible. 5 Kinetic energy at the diffuser exit is negligible. 6 There are no

work interactions.

Analysis We take the diffuseras the system (Fig. 5–26). This is a control

volumesince mass crosses the system boundary during the process. We

observe that there is only one inlet and one exit and thus m. 1 m. 2 m..

(a) To determine the mass flow rate, we need to find the specific volume

of the air first. This is determined from the ideal-gas relation at the inlet

conditions:

Then,

Since the flow is steady, the mass flow rate through the entire diffuser remains

constant at this value.

(b) Under stated assumptions and observations, the energy balance for this

steady-flow system can be expressed in the rate form as

Rate of net energy transfer Rate of change in internal, kinetic,

by heat, work, and mass potential, etc., energies

The exit velocity of a diffuser is usually small compared with the inlet

velocity (V 2 V 1 ); thus, the kinetic energy at the exit can be neglected.

The enthalpy of air at the diffuser inlet is determined from the air table

(Table A–17) to be

h 1 h (^) @ 283 K283.14 kJ/kg
h 2 h 1

V 22
V 12
2
m

ah 1 
V 12
2
bm

ah 2 
V 22
2
b¬¬ 1 since Q

0, W

0, and ¢pe 02
E

inE

out
E

in
E

out^ ^ dEsystem>dt^ ^0
m


1
v 1
¬V 1 A 1 
1
1.015 m^3 /kg
¬ 1 200 m/s 21 0.4 m^22 78.8 kg/s
v 1 
RT 1
P 1

0.287 kPa#m^3 /kg#K 21 283 K 2
80 kPa
1.015 m^3 /kg
234 | Thermodynamics
Nozzle V 2 V 1
V 1 V 1
V 1
Diffuser V 2

FIGURE 5–25
Nozzles and diffusers are shaped so
that they cause large changes in fluid
velocities and thus kinetic energies.
AIR
T 2 =?
P 1 = 80 kPa
T 1 = 10°C
V 1 = 200 m/s
A 1 = 0.4 m^2
m =?
FIGURE 5–26
Schematic for Example 5–4.
0 (steady)
⎭⎪⎪⎬⎪⎪⎫ ⎭⎪⎪⎪⎬⎪¡⎪⎪⎫