What is the difference between thermodynamic efficiency and efficiency?
This text is generated by AI trained by Professor Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
In fluid mechanics, the term “efficiency” can refer to different concepts depending on the context. So the two terms you use might be the same or might be different, depending on the context.
- Thermodynamic Efficiency: This is a measure of how well a system converts energy from one form to another, based on the principles of thermodynamics. It is often defined as the ratio of useful work output to the total energy input. For example, in a desk fan, energy is added to the air in the form of increased pressure and/or axial speed (useful work) and also swirl and heat (not useful). The fraction of the energy that goes into useful work is the thermodynamic efficiency of the fan:
\eta_\mathrm{thermo} = \frac{\text{power added to fluid}}{\text{power supplied to fan by motor}}
The motor also sinks energy as heat and it has a thermodynamic efficiency also, and the thermodynamic efficiency of the motor-driven fan is the product of the thermodynamic efficiencies of each component.
- Propeller Efficiency: The exact same geometry, in the context of an airplane propeller, is often evaluated not in terms of the thermodynamic efficiency of the rotor, but instead the propeller efficiency of the rotor (or sometimes this is called the propulsive efficiency)
\eta_\mathrm{propeller} = \frac{\text{power added to vehicle}}{\text{power supplied to fan by motor}}
The power added to the vehicle is given by F_T U_\text{vehicle}, the product of the thrust force and the vehicle speed. That power is always lower than the power added to the fluid by a factor \frac{U_\text{vehicle}}{U_\text{rotor}}, where U_\text{rotor} is the speed of the fluid at the rotor.
The difference is what you care about – do you care about adding energy to the fluid, or do you care about the effect of that power transfer on the vehicle. A motionless vehicle with its propellers running is not generating any vehicle motive power and that system has a propulsive efficiency of zero, no matter how well the propellers are moving fluid around.
To formulate this response, I reviewed the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked their significance below. If they are marked as relevant, I encourage you to take a look at them:
Textbook sections:
- Chapter 2.1: Turbomachines Part 1 (RELEVANT)
- Chapter 2.6: Turbomachine Inefficiencies (RELEVANT)
- Chapter 6 Fundamentals: Combining the language of fluid mechanics with the language of hydraulics en… (RELEVANT)
- Chapter 2.2: Nondimensional Turbomachine Parameters (RELEVANT)
- Chapter 2.1: Turbomachines Part 2 (RELEVANT)
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