The system efficiency, as defined by the power transfer in and out of the example diagram in the equations, is:
where HS is static head, which includes elevation and pressure head.
Pe is motor input power.
Pf is fluid power.
PS is shaft power.
Q is volumetric flow rate delivered to the tank.
ηsys is overall system efficiency.
γ is fluid specific rate.
The flow rate is the net flow between tanks (ignoring recirculation flow).
The head is the elevation difference between the tanks, or static head (implicitly ignoring friction losses). This is a true system efficiency — it overlooks the details and sees only the big picture. This approach can be quite useful. However, it does not work for all situations. For example, the equation will produce a system efficiency of zero for a closed cycle circulating system with no static head.