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Fan Law Calculator

Run the Fan Law Calculator MicroSim Fullscreen

This sketch is built on the FanPedia MicroSim kit. To run it in the p5.js editor, add the ../shared-libs/ files it loads (fanpedia-sim.css, fanpedia-core.js, fanpedia-p5.js, fan-models.js, fan-curves.js), or their published URLs, to the editor's index.html before pasting ch25-fan-law-calculator.js.

About This MicroSim

This calculator applies the three fan laws to Curve A, the illustrative fan curve from Chapter 10. The base fan runs at 1,380 RPM on standard air and operates at 10,000 CFM, 4.0 in. wg and 9.0 BHP, at 70% static efficiency, on the system curve P = 4.0 × (Q ÷ 10,000)².

Every point of Curve A is mapped through the fan laws for geometrically similar fans:

  • Airflow: Q2 = Q1 × (N2/N1) × (D2/D1)³
  • Pressure: P2 = P1 × (N2/N1)² × (D2/D1)² × (ρ2/ρ1)
  • Power: BHP2 = BHP1 × (N2/N1)³ × (D2/D1)⁵ × (ρ2/ρ1)

Static efficiency at mapped (corresponding) points is unchanged. The readout panel shows the base and new speed, airflow, static pressure, BHP and static efficiency, with the ratio between them, so you can see at a glance that power moves with the cube of speed and the fifth power of diameter.

The sim starts with four challenges, in this order. Each one asks for a single number:

# Question Model answer
1 The same system needs 11,500 CFM. What speed? 1,587 RPM
2 At 1,587 RPM, what BHP? 13.69 BHP
3 The fan is slowed to 1,104 RPM. What static pressure (in. wg)? 2.56 in. wg
4 The next size up has a diameter ratio of 1.12 and runs at 1,380 RPM. What BHP at the corresponding point? 15.86 BHP

An answer is correct when it is within 2% of the model answer. You get two attempts; a wrong answer shows the worked fan-law calculation, and a second wrong answer shows the model answer and the challenge counts as missed. When a challenge is resolved, the sim sets the matching ratio, shows your answer beside the model answer, and draws the new curve (solid indigo) and the new operating point (orange diamond) beside Curve A (solid grey) and its base operating point (dark dot). The ratio sliders are locked until all four challenges are done; then Explore mode unlocks. Mastery is 4 of 4 on the first attempt. Explore mode is never scored.

Notes on the model:

  • Curve A is illustrative, not a catalog curve. Its 9.0 BHP is rounded, so Q × P ÷ (6,356 × BHP) gives 69.9%; the sim uses the stated 70% as the base efficiency and carries it unchanged to every corresponding point.
  • A change in air density scales the system's resistance as well as the fan's pressure, so the sim draws a second, density-scaled system curve (orange, dashed). The corresponding point stays on it at the same CFM.
  • With a diameter change, the orange point is the fan-law corresponding point. It no longer lies on the original system curve, and the sim says so.

How to Use

  1. Read challenge 1, type a number in Your answer and press Check (or Enter).
  2. A correct answer reads "✓ Correct: model answer." in a solid green box. A wrong one reads "✗ Not quite." with the worked calculation in a dashed red box; use the second attempt.
  3. Press Next challenge (or Enter) and repeat for challenges 2 to 4. "Challenges correct: n of 4" keeps the running score.
  4. After challenge 4, press Start exploring. The panel shows the first-attempt score and the mastery line. Move the speed ratio alone and watch the orange operating point slide along the system curve while efficiency stays at 70.0%. Then try the diameter and density ratios. Reset ratios to 1.00 returns to Curve A; Start over clears the score and returns to challenge 1.

Keyboard: Enter checks the answer, and Enter again goes to the next challenge. Tab reaches the answer box, every button and the three sliders; the arrow keys move a focused slider.

Data label: "Illustrative values · Curve A, Chapter 10", at the bottom left of the drawing.

Iframe Embed Code

You can add this MicroSim to any web page by adding this to your HTML:

<iframe src="https://moroshek.github.io/FanTASTIC-textbook/sims/ch25-fan-law-calculator/main.html"
        height="642px"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Learning Objective

The learner will solve fan-law problems for a new speed, pressure or brake horsepower after a change in speed, impeller diameter or air density, to within 2% of the model value (Bloom: Apply, verb: solve).

Audience

Adult professional development: new application engineers, sales staff, representatives and facilities staff who have read the fan-law section of Chapter 25 and the fan-curve material in Chapter 10.

Duration

10-15 minutes

Prerequisites

  • Fan laws, speed change calculation and size change calculation (Chapter 25)
  • Fan curve, system curve and static efficiency (Chapter 10)
  • Density correction factor (Chapter 10)

Activities

  1. Challenges (5-8 min): Solve the four challenges with a calculator before pressing Check. Write down the ratio and exponent used for each.
  2. Exploration (3-5 min): Change only the speed ratio and record airflow, pressure, BHP and efficiency at 0.80, 1.00 and 1.15. Confirm that BHP at 0.80 is 0.512 of the original.
  3. Misconception check (2 min): Set the density ratio to 0.80 and explain why the CFM does not change. Set the diameter ratio to 1.25 and explain why airflow nearly doubles rather than rising by 25%.

Common Misconceptions Addressed

  • Power rises in proportion to speed (it rises with speed cubed).
  • Doubling the diameter doubles the airflow (airflow goes with diameter cubed).
  • Changing speed changes efficiency on a pure-resistance system (it does not; the point slides along the system curve).
  • Hotter, lighter air changes the CFM a fan moves (it changes pressure and power, not CFM).

Assessment

  • The running line "Challenges correct: n of 4" counts challenges solved on either attempt. At the end the sim shows "First-attempt score: n of 4" and the mastery line; mastery is 4 of 4 challenges answered within 2% of the model value on the first attempt.
  • Moving the ratio sliders in Explore mode is not evidence of mastery. Ask the learner to explain, from the exponents, why 15% more airflow needs about 52% more power.

References

  1. Affinity laws - Wikipedia overview of the fan and pump affinity laws for speed and diameter changes.
  2. FanPedia: The Fan & Blower Encyclopedia - Twin City Fan's reference on fan performance, fan laws and system effect.
  3. AMCA International - publisher of the fan application manuals and test standards that use the fan laws to adjust rated performance.