Shortcomings of the above analysis
It is assumed in the above analysis that the expansion is a constant
enthalpy process. This is strictly not true inside a capillary tube since there is a
large change in kinetic energy due to change in velocity along the length due to
flashing of refrigerant liquid. In fact kinetic energy increases at a very fast rate as
the velocity becomes sonic and the flow becomes choked. First law of
thermodynamics indicates that in absence of heat transfer, work done and
change in potential energy for a system in steady state, the sum of enthalpy and
the kinetic energy must remain constant. Hence, if the kinetic energy increases
the enthalpy must decrease, as a result the quality of the refrigerant will be lower
than calculated by assuming constant enthalpy. The actual state of refrigerant in
a constant diameter adiabatic tube is represented by Fanno line, which is shown
in Fig.24.6 on h–s diagram along with the saturation curve. Fanno line is the
solution of steady, compressible adiabatic flow with friction through a tube of
constant diameter.
It is observed that in the early part of the capillary tube, the constant
enthalpy line does not deviate very much from the Fanno line. In the latter part,
the deviation from the Fanno line increases. Most of the length of the capillary
tube happens to be in the latter portion where quality and velocity changes are
very significant; hence constant enthalpy approximation may introduce significant
error.