Modern Engineering Thermodynamics

6.5 Nozzles and Diffusers 175
m
(a) Nozzle
FIGURE 6.3
Nozzles and diffusers.
±Q
m
±Q
W = 0 W = 0
(b) Diffuser
diffusers perform opposite functions. In their simplest
form, a nozzle is merely a converging duct and a diffuser
is merely a diverging duct, as shown schematically
in Figure 6.3. 3
Most commercial nozzles and diffusers are well insulated
(adiabatic). However, they need not be, and therefore
may have either a heat loss or a heat gain. On the
other hand, the simple mechanical nature of nozzles
and diffusers prevents them from either performing or
absorbing work. Therefore, they can generally be taken
to be aergonic devices.
Since both nozzles and diffusers are clearly single inlet, single outlet devices, we can carry out an analysis of their
steady state operation by using the modified energy rate balance of Eq. (6.12). Also, both nozzles and diffusers
are either oriented horizontally, as shown in Figure 6.3, so that Z in = Z out or have such small changes in height
between the inlet and outlet that the enthalpy change dominates the specific potential energy change, as discussed
previously. This allows us to neglect the change in flow stream specific potential energy in nozzle and diffuser
analysis.
However, the flow stream specific kinetic energies are not necessarily negligible, because in both nozzles and
diffusers, at least one of the flow streams normally has a high velocity. Consequently, we ignore the low-speed
flow stream specific kinetic energy in each case and set V in ≈ 0 for the nozzle and V out ≈ 0 for the diffuser.
At this point, we have developed the following set of assumptions for these devices:
Nozzle
Diffuser
_W = 0 _W = 0
Z in − Z out ≈ 0 Z in − Z out ≈ 0
V in ≈ 0 V out ≈ 0
Applying these assumptions for nozzles to the modified energy rate balance of Eq. (6.12) gives the following
results:
or
_Q − 0 _mðh in − h out − V 2 out /2g c + 0Þ = 0
V out
= ½2g c ð _Q / _m + h in − h out ÞŠ 1/2 (6.15)
nozzle
Notice that adding heat to the nozzle increases the outlet velocity, whereas removing heat decreases it. If the
nozzle is insulated (adiabatic), then _Q = 0 and
p
V out
= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2g c ðh in − h out Þ
(6.16)
adiabatic
nozzle
Applying the previous assumptions for diffusers to the modified energy rate balance of Eq. (6.12) gives the
following results:
_Q + _m h in − h out + V 2 in /2g c
= 0
or
h out
= h in + Vin 2 /2g c + _Q / _m (6.17)
diffuser
Thus, heat added to a diffuser increases the outlet specific enthalpy, whereas heat removal reduces it. For an
insulated (adiabatic) diffuser, we have
h out
= h in + V adiabatic
in 2 /2g c (6.18)
diffuser
3 This figure is accurate only for subsonic flow. When the flow becomes supersonic, the relative shapes of nozzles and diffusers are not
the same as those shown here.