With the definition of the work coefficient in (6.4a) and (6.4b), we can now write from (4.22a) to (4.22d) the nondimensional azimuthal velocity component expressions as follows: $$ \frac{{{{c}_{\rm{u1}}}}}{u} = \left( {1 - \hat{r}} \right) - \frac{\Psi}{4} $$ $$ \frac{{{{c}_{\rm{u2}}}}}{u} = \left( {1 - \hat{r}} \right) + \frac{\Psi}{4} $$ $$ \frac{{{{w}_{\rm{u1}}}}}{u} = \hat{r} + \frac{\Psi}{4} $$