How is the fan efficiency zero at the highest flowrate point (at which there is zero pressure rise)? I know the fan efficiency is given as
$fan\_efficiency = output\_power/input\_power$
where output_power of the fan is given
$Output\_Power = Pressure\_rise \ \times \ Flow\_rate$
But even if there is no pressure rise across a fan, the fan does cause the flow to happen by transferring energy (or power) to the fluid. So why is the efficiency zero (and also the $fan\_output\_power$ zero) at the highest flow rate point?