Modern Engineering Thermodynamics

180 CHAPTER 6: First Law Open System Applications
A throttling device may be thought of as any aergonic device whose primary purpose is to offer a resistance to
flow. Throttles may or may not be insulated. But they are usually such small devices and have such high flow
ratesthattheresidencetimeofthefluidinthemistooshortforsignificantheattransportofenergytooccur.
Consequently, a throttling device is commonly taken to be adiabatic regardless of whether it is actually insulated
or not.
The small physical size of most throttling devices also prevents them from having a significant change in
specific potential energy between their inlet and outlet flow streams. However, a throttle need not have the
same inlet and outlet flow velocities, and therefore, it may have a significant specific kinetic energy change
across it.
Consequently, we define a throttling device with the following set of thermodynamic conditions:
Throttling Devices Have
_Q = 0
_W = 0
Z in − Z out ≈ 0
Applying these conditions to the modified energy rate balance of Eq. (6.12) gives
or
0 − 0 + _m½h in − h out + ðV 2 in − V2 out Þ/2g c + 0Š = 0
h out = h in + ðV 2 in − V2 out Þ/2g c (6.23)
If V in = V out , as when the fluid is incompressible and the inlet and outlet areas of the throttle are equal
(e.g., cases a–d in Figure 6.5), then Eq. (6.23) reduces to the simpler form
h out = h in (6.24)
Such throttling devices are said to be isenthalpic (i.e., they have a constant enthalpy).
Even if the inlet and outlet velocities are clearly unequal in some problem, you may still be able to justify using
the simpler Eq. (6.23) as the result of your analysis. The high-velocity flow stream of an unequal area throttling
device is always limited by the speed of sound in the flowing medium. 5
Consequently, if h is large, say on the order of 1000 Btu/lbm (2300 kJ/kg), then the specific kinetic energy of
the flow stream can never be more than 2 or 3% of this value and may therefore be considered negligible. The
rule of thumb discussed earlier in this chapter can be applied as follows: If you are given a throttling device problem
without adequate velocity information and where a velocity is not an unknown that you are required to find as part of the
solution, then you should assume that the specific kinetic energy terms are either equal (and therefore cancel each other) or
that they are negligible.
For an incompressible fluid flowing through a throttling device, we can use Eq. (6.19) in Eq. (6.23) to produce
cðT in − T out Þ + vðp in − p out Þ + ðV 2 in − V2 out Þ/2g c = 0
andifweneglectthespecifickinetic energy terms (or have V in = V out ), then this equation can be rearranged
to give
T out = T in + ðv/cÞðp in − p out Þ
and since p in is usually greater than p out ,thisequationtellsusthatthereis normally a temperature rise
in an incompressible fluid flowing with a negligible specific kinetic energy change through a throttling
device.
5 Supersonic nozzles or diffusers usually have a flow stream velocity greater than the sonic velocity. But, with the rare exception of
supersonic flow at the inlet to a throttling device, subsonic flow prevails throughout throttling devices.