For all the analysis to find work done by a compressor or work done on a turbine, the book I'm reading (Fundamentals of Turbomachinery by Venkanna B.K) uses the Euler turbine and pump equation, $$W=\dot{m}(V_{w1}U_1\pm V_{w2}U_2) $$ where $V_w$ is the whirl velocity of fluid at inlet and exit, and $U$ is the mean rotational speed of the rotor blades and inlet and exit. It is based on the conservation of angular momentum of the fluid by drawing velocity triangles.
While this might give the value of work done due to momentum of the fluid, what about the work done by the pressure energy in the fluid or work done to increase the pressure energy of the fluid? Especially in cases like Francis turbine and axial compressors where change in pressure energy plays a big role, how can we consider only the momentum of the fluid in our analysis? I'm guessing work needs to be done to increase the pressure energy as well/work is done by pressure energy in turbines like Francis turbine.
Maybe because of complicated aerofoil shapes of the blades its hard to do an analytical approach but shouldn't we at least account for a factor of change in pressure energy?