Step 1: Define Work-Done Factor.
The work-done factor, \(\Psi\), in turbo machinery is a dimensionless parameter that indicates the ratio of actual work done to the ideal work possible in an isentropic process.
Step 2: Analysis for Isentropic Flow.
In a truly isentropic process within a turbo machine, where there are no losses and the process is reversible, the actual work equals the ideal work, hence \(\Psi = 1\).