Open System

Work interactions to the steady flow system consists of two parts, the shaft work (\(W_s\)), and the flow work (\(W_{\text{flow}}\)). Shaft work is done by the shaft protruding outside the system, say through a compressor, pump, turbine. Work is also done on the system by the incoming fluid by the amount \(P_1V_1\), and, in a similar way work is done by the system by the amount \(P_2V_2\) to send the fluid at the outlet. The difference (\(P_1V_1-P_2V_2\)) is the net flow work done (\(W_{\text{flow}}\)) on the system. Therefore, the first law becomes \[\Delta U = Q + W_s + W_{\text{flow}}\] where \(\Delta\) = Out \(-\) In; or, State 2 \(-\) State 1. \[U_2-U_1 - W_{\text{flow}} = Q +W_s\] i.e., \[U_2-U_1 - (P_1V_1 - P_2V_2) = Q +W_s\] From the definition of enthalpy, \(H=U+PV\), the above equation reduces to \[H_2-H_1 =\Delta H= Q+W_s\] By using the enthalpy instead of the internal energy to represent the energy of a flowing fluid, one does not need to be concerned about the flow work.

For steady state flow processes, by including the kinetic and potential energy changes, we can write \[\Delta H + \frac{\Delta u^2}{2} + g\Delta z = Q + W_s\] where

\(u\) = velocity
\(W_s\) = shaft work

The above equation is called as Steady-state Steady-flow Energy Equation.