I have a fan, it’s CFM, power draw, rpm and wind load. How do I calculate the efficiency?
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
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PURPOSE OF THE EXERCISE:
Demonstrate how to use system-level conservation principles (mass, momentum, and energy) to connect measured airflow, wind load, rpm, and power draw to a fluid–mechanical efficiency estimate for a fan. -
ENGINEERING CONTEXT:
In fan and propeller design, efficiency is evaluated by comparing the useful work imparted to the fluid (thrust times an effective airspeed) to the shaft power input. Mastering this analysis allows one to size, optimize, or select fans for applications such as ventilation, cooling, or propulsion. -
PHYSICAL CONTEXT:
The dominant physics involve converting rotational motor work into an increase in fluid kinetic energy and pressure difference (thrust), as captured by conservation of momentum and Bernoulli’s relation along streamlines (away from the fan where work is done). -
ASSUMPTIONS:
Assume steady, quasi–one-dimensional, incompressible and inviscid flow near the fan; these assumptions are reasonable at high Reynolds numbers and when the control volume is chosen close enough to the fan that viscous effects are minimal. -
SOLUTION TECHNIQUE:
A student should first sketch a control volume encompassing the fan to visualize the momentum flux and pressure force. With the available data we proceed as follows:
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Use the measured wind load as the thrust force, F_T.
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Recognize that the fan’s useful fluid power is given by
P_\mathrm{fluid}=F_T\,U_\mathrm{prop}\,,
where U_\mathrm{prop} is the characteristic air speed at the fan. This speed may be estimated from the volumetric flow rate (converted from CFM) via
\dot{m}=\rho\,Q\quad\text{and}\quad F_T=\dot{m}\,\Delta U\,,
or by relating the induced velocity directly from control–volume analysis when a proper scheme is identified.
- Efficiency is defined as the ratio of fluid power output to shaft power input:
\eta=\frac{P_\mathrm{fluid}}{P_\mathrm{shaft}}=\frac{F_T\,U_\mathrm{prop}}{P_\mathrm{shaft}}\,.
- The rpm helps indicate the fan’s operating speed and, together with geometric or empirical relations, can further refine the estimate of U_\mathrm{prop}.
- REFLECTION:
This methodology quantitatively connects measured fan parameters—CFM, wind load, power draw, and rpm—to the efficiency of energy conversion from shaft power to fluid power. The analysis is accurate as long as the control volume boundaries are chosen to capture the dominant momentum flux and the quasi–1D assumptions hold.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 2 How Stuff Works: How a propeller works (RELEVANT)
- Chapter 2.2: Nondimensional Turbomachine Parameters Part 2 (RELEVANT)
- Chapter 2.1: Turbomachines Part 3 Part 1 (RELEVANT)
- Chapter 2.6: Turbomachine Inefficiencies (RELEVANT)
- Chapter 2 How Stuff Works: How a wind turbine works (RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.
Hi PK Bot – it seems like from your calculations that if you had the fan diameter and therefore cross-sectional area, you could determine the speed at the propeller, which would then directly give the power, which would then directly give the efficiency. and you shouldn’t need the rpm for the calculatoin. what do you think. if you agree can you show OP the equations
This text is generated by AI trained by Professor Brian J. Kirby on his lectures, videos, notes, message board responses, and textbook
PK Bot’s answer:
Below is one way to arrive at an efficiency expression that does not explicitly require rpm. Assume you have measured the volumetric flow rate Q, the fan (or propeller) cross‐sectional area A, and the thrust (wind load) F_T. Then the characteristic speed at the fan is
U_\mathrm{prop}=\frac{Q}{A}\,.
The useful fluid (or kinetic) power is the product of thrust and this induced speed:
P_\mathrm{fluid}=F_T\,U_\mathrm{prop}\,.
The efficiency is given by
\eta=\frac{P_\mathrm{fluid}}{P_\mathrm{shaft}}=\frac{F_T\,U_\mathrm{prop}}{P_\mathrm{shaft}}\,.
Thus, once you know A, Q, and F_T, you can compute U_\mathrm{prop} and then the fluid power, without requiring the rpm directly. In a control-volume analysis the rpm information is more useful when you need to relate blade geometry or induced velocity profiles to the flow—for example, via quasi–one-dimensional momentum and energy balances. However, when you can directly measure the mass flow (\dot{m}=\rho Q) and the thrust, the induced speed and therefore the efficiency are determined purely from these global balance equations.
So in summary:
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Get the induced fan speed from the flow:
U_\mathrm{prop}=\frac{Q}{A}\,. -
Compute the fluid power:
P_\mathrm{fluid}=F_T\,U_\mathrm{prop}\,. -
And then the efficiency is
\eta=\frac{P_\mathrm{fluid}}{P_\mathrm{shaft}}\,.
This shows that if you have a known fan area and measured flow rate and thrust, the rpm is not needed to calculate the efficiency through this system-level control volume analysis.
In formulating this response, I consulted the 2025 edition of Professor Kirby’s textbook (Vol 1 | Vol 2), and I have ranked the sections based on their relevance. If they are marked as relevant, I encourage you to explore them:
Textbook sections:
- Chapter 2 How Stuff Works: How a propeller works (HIGHLY RELEVANT)
- Chapter 2.2: Nondimensional Turbomachine Parameters Part 2 (HIGHLY RELEVANT)
- Chapter 7.1: Helicopter/Quadcopter Rotors Part 4 Part 1 (HIGHLY RELEVANT)
- Chapter 7.1: Helicopter/Quadcopter Rotors Part 5 (HIGHLY RELEVANT)
- Chapter 9.6: Centrifugal Pump Design Part 1 (RELEVANT)
Disclaimer:
See What is Professor Kirby Bot for information about Professor Kirby Bot and its answers.