Modern Engineering Thermodynamics

6.9 Shaft Work Machines 187
6.9 SHAFT WORK MACHINES
Shaft work machines are devices whose primary function is to promote a work input or output through a rotating
or reciprocating shaft. Common shaft work machines are hydraulic pumps, pneumatic compressors and fans,
gas or hydraulic turbines, electric motors and generators, and external and internal combustion engines. Most
shaft work machines are steady state, steady flow, single-inlet single-outlet devices (electric motors and generators
are exceptions, since they have no flow streams). The work produced or absorbed by such devices can then
be determined from the MERB of Eq. (6.12) as
_W shaft = _m½h in − h out + ðV 2 in − V2 out Þ/2g c + ðZ in − Z out Þg/g c Š + _Q (6.30)
This equation shows that the effect of heat loss ð _Q < 0Þ from a work-producing device ( _W > 0) is to reduce the
device’s power output. Therefore, most work-producing systems (engines, turbines, etc.) are insulated to
improve their efficiency. Similarly, heat loss from a work-absorbing device (such as a compressor) requires
that more work be supplied to produce the same state change in the flow streams. Consequently, most of
these devices are also insulated to increase their efficiency. Massive amounts of heat loss from these systems
by external cooling usually indicate the need to lower their internal temperatures due to the existence of large
internal irreversibilities. This is a consequence of the second law of thermodynamics and is discussed in the
next chapter.
Most shaft work machines have negligible change in the specific kinetic and potential energies of their flow
streams. Obvious exceptions are hydroelectric water turbines, in which the specific potential energy change of
the water is the energy source for the turbine, and windmills, in which the specific kinetic energy change of the
air is the energy source for the windmill. The resulting ERB for an insulated shaft work machine with negligible
changes in specific kinetic and potential flow stream energies, operating in a steady state, steady flow, singleinlet,
single-outlet manner is obtained from Eq. (6.30) as
_W shaft = _mðh in − h out Þ (6.31)
Figure 6.11 illustrates the graphical symbols used to represent several common shaft work machines.
If an incompressible fluid is used in a shaft work machine described by Eq. (6.31), then Eq. (6.19) can be used
to describe the change in specific enthalpy as
_W shaft
incomp:
fluid
= _m½cðT in − T out Þ + vðp in − p out ÞŠ
Normally, there is very little temperature change across such devices as hydraulic pumps, motors, and turbines,
so that the previous equation reduces to
_W shaft
isothermal
incomp:
fluid
= _mvðp out − p in Þ (6.32)
Notice that, in this equation,
_mv = ðρAVÞv = AV v
ðvÞ = AV
where AV is the volume flow rate.
If an ideal gas with constant specific heats is used in a shaft work machine described by Eq. (6.31), then
Eq. (6.22) can be used to describe the change in specific enthalpy, and Eq. (6.31) becomes
_W shaft
ideal
gas
= _mc p ðT in − T out Þ