(B) Quality degradation for a flow with friction

Consider a steady and adiabatic flow of an ideal gas through the segment of a pipe. Applying the first law of thermodynamics between sections (1)-(1) and (2)-(2) (Fig. 1.28)

Fig. 1.28 Adiabatic steady flow of an ideal gas in a straight pipe

h1 = h2

1.231

Applying T-dS relationship

Tds = dh - vdp

1.232

or,

1.233

or,

1.234

1.235

where since and higher order terms are neglected. Hence, lost work or irreversibility is

1.236

Hence decrease in exergy is proportional to the pressure drop as well as mass flow rate.

(c) Mixing of two fluid streams

Two fluid streams 1 and 2 of an incompressible fluid or ideal gas mixing adiabatically at constant pressure as shown in Fig. 1.29.

Fig. 1.29 Mixing of two fluid streams