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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?

Ref: https://www.linquip.com/blog/fan-efficiency/

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    $\begingroup$ The mathematical expression explains it. The dimensionless expression for efficiency you show implies, at the right end of the curve, that the fan is consuming power to keep turning, but is not adding any power to the air flow. I.e. an external device would be doing the work to blow the air into the input already at the maximum velocity. This efficiency expression is dimensionless, which is nice for theory. You could use another figure of merit, such as air flow per power input, for a particular input and output condition (eg open air, or in some duct geometry that your system has). $\endgroup$
    – Pete W
    Commented Mar 23 at 14:31

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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.

Don't assume that the flow in that graph is driven by the fan -- if the fan efficiency is going to zero, that means it is not exerting any net axial force on the airflow. That, in turn, means that the air is being driven by some other mechanism.

The fan may be inducing turbulence in the fluid, and that is, indeed, adding energy to the flow.

However, in that context, the authors clearly mean that the useful action of the fan is to induce flow -- if there's no pressure rise across the fan, then for the purposes of inducing flow it may as well not be there -- so it's consuming a finite amount of power to turn, and generating zero effect. Zero effect for finite effort means zero efficiency.

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  • $\begingroup$ But the graph shows there is flow taking place across the fan plane and not just turbulent dissipating the energy. Isn't this considered a 'useful action'? $\endgroup$
    – GRANZER
    Commented Mar 23 at 20:08
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    $\begingroup$ See my edits. These sorts of graphs come about because someone makes the driven quantity (airflow in this case) equal some number. Somewhere in the experimental setup, there's another fan. $\endgroup$
    – TimWescott
    Commented Mar 23 at 20:24

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