In open systems (ones where material flows into and out of our process), we need to recall that takes energy (work) to make material flow! (Recall that you need to squeeze the toothpaste tube to get the stuff to flow out.)
The work term, therefore can be broken into a "shaft" component and a "flow" component:
Flow work is the energy necessary to cause flow in an open system.
Shaft work is any mechanical energy other than that necessary for flow. Typically this requires a stirrer or turbine (hence the name "shaft" work).
Mathematically, the differing types of work can be expressed
W = Ws + Wf = Ws + $\Delta$ (PV)
The simplest way to account for this is to use enthalpy in open systems rather than energy since H = U + PV, in order to account for both internal energy and flow work at the same time.
Explain the difference between shaft work and flow work