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I often see the term "net mechanical efficiency" used in literature, but I am not quite sure what it means, and what the difference is between it and "normal" efficiency. Take this sentence for example: ... increased the effectiveness, while reducing net mechanical efficiency. What does exactly does this mean?

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Mechanical efficiency is usually used as a metric to account for frictional losses in systems. For example, the transmission of a car transmits mechanical work from the engine to the wheels so the mechanical efficiency of the system will be $W_{transmitted}/W_{received/ideal}$. Even within an engine, there is friction between the piston and cylinder walls, bearings of crankshafts etc. Mechanical efficiency is: $W_{output}/W_{obtained\;from\; gas}$. The denominator is the work obtained from the work-fluid, the thermodynamic cycle. Therefor it is a way to quantify the frictional loses in the system.

What I have mentioned above is one of the common use of this term, but there could be other definitions too. You need to look into the context of usage

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