Air Density Ratio Explorer¶
Run the Air Density Ratio Explorer MicroSim Fullscreen
About This MicroSim¶
Fan catalogs are printed at standard air: 70°F at sea level, 0.075 lb/ft³. Real jobs are hotter, colder or higher. The density ratio (DR) is the actual density divided by standard density:
where \( T \) is the air temperature in °F and \( h \) is the site altitude in feet. At a fixed speed a fan moves the same CFM in thin air or thick air, while its static pressure and brake horsepower scale with DR. That gives two rules: to predict what a fan really develops at the job, multiply the catalog value by DR; to select from a standard-air catalog, divide the required actual pressure by DR.
The chart plots DR against air temperature from −20°F to 600°F for four site altitudes (0, 2,000, 5,000 and 8,000 ft). The temperature and altitude sliders move a marker (✕) to any setting. A reference panel lists the altitude pressure ratios from 0 to 10,000 ft.
Four challenges, in this order, ask for six entries:
| # | Situation | Asked | Model answer |
|---|---|---|---|
| 1 | 250°F at sea level; catalog shows 4.0 in. wg at standard air | Density ratio; actual SP | 0.746; 2.99 in. wg |
| 2 | 70°F at 5,000 ft; job needs 2.0 in. wg actual | Density ratio; catalog SP to select at | 0.832; 2.40 in. wg |
| 3 | 120°F at 5,000 ft | Density ratio | 0.760 |
| 4 | 600°F at sea level | Density ratio | 0.500 |
A ratio is correct within ±0.005 and a pressure within ±0.03 in. wg of the unrounded model value. Each entry has two attempts. For challenges 1 and 2 you type both boxes and press Check; the pressure is checked once the ratio is right or revealed. A correct entry shows "✓ Correct:
During the challenges the chart shows the shape of the curves and the marker's position, but no numeric ratio: read the curve against the axis to sanity-check your calculation. After challenge 4, Explore mode (never scored) unlocks the exact readouts. Hovering the chart shows DR to 3 decimals and density to 4 decimals for each altitude, and the marker readout shows the temperature factor, the pressure ratio, the density and what a fan rated 4.00 in. wg at standard air develops there, at the same CFM and RPM.
How to Use¶
- Read challenge 1. Move the Air temperature and Site altitude sliders so the marker sits at the stated condition, and note roughly where it falls on the axis.
- Calculate the density ratio (and, for challenges 1 and 2, the corrected pressure). Type the answers and press Check (or Enter).
- Read the feedback. If you have an attempt left, fix the step it names and check again.
- Press Next challenge. After challenge 4, read the summary.
- In Explore mode, hover the curves and move the marker. Compare 250°F at sea level with 70°F at 8,000 ft: two very different jobs with nearly the same density. Press Start over to repeat the challenges.
Keyboard: Tab reaches every control. Enter in an answer box checks it; after an entry is settled, Enter goes to the next challenge. The arrow keys move a focused slider.
Data label: "Curves from DR = 530 ÷ (T + 460) × (1 − 6.8754 × 10⁻⁶ × h)^5.2559 · Catalog pressures in challenges 1 and 2 are illustrative values", shown under the chart.
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/ch01-air-density-ratio-explorer/main.html"
height="1032px"
width="100%"
scrolling="no"></iframe>
Lesson Plan¶
Learning Objective¶
The learner will calculate the density ratio for a stated air temperature and site altitude, and use it to correct a static pressure between catalog and job conditions, to within ±0.005 on the ratio and ±0.03 in. wg on the pressure (Bloom: Apply, verb: calculate).
Audience¶
Adult professional development: new application engineers, sales staff, representatives and facilities staff.
Duration¶
10-15 minutes
Prerequisites¶
- Air density and standard air (70°F, sea level, 0.075 lb/ft³)
- Density ratio, air temperature, altitude and absolute pressure
- Static pressure
- The two correction rules: multiply to predict, divide to select
All are covered in the Chapter 1 sections "Air Density", "Air Temperature" and "Altitude".
Activities¶
- Challenges (8 min): Place the marker first, then calculate and check each entry. Two attempts each.
- Explore (4 min): Hover the curves at 250°F and 600°F. Then find an altitude where 70°F air is as thin as 120°F air at sea level.
- Discussion (3 min): A fan selected for a 5,000 ft site straight from the catalog at 2.0 in. wg: is it short of pressure or oversized, and by how much?
Common Misconceptions Addressed¶
- Hot air or high altitude reduces the CFM a fan moves at a given speed: the Explore readout states that CFM and RPM stay the same while pressure and BHP scale with DR.
- The temperature correction can be done in °F directly (70 ÷ 250): challenge 1 recognizes 0.28 and points to absolute temperature; challenge 4 recognizes a missing 460.
- To select a fan for thin air you multiply the required pressure by DR: challenge 2 recognizes the multiplied answer and explains that it would undersize the fan.
Assessment¶
- Running score shown as "Entries correct: n of 6"; mastery is 6 of 6 entries correct within two attempts each. The summary shows "Mastery reached (6 of 6 needed)." or what is still needed, and lists any missed entry with its calculation.
- Explore mode is not evidence of mastery. Follow up: a motor sized only for the hot running condition of challenge 1 starts up cold. What happens to its load?
References¶
- Chapter 1: Air, Pressure and the Fan - The sections "Air Density", "Air Temperature" and "Altitude", with the worked examples behind the challenges.
- FanPedia online, Twin City Fan - The fan and blower encyclopedia this textbook is built from.
- Density of air, Wikipedia - How air density depends on temperature and pressure.
- Barometric formula, Wikipedia - The standard-atmosphere relation behind the altitude pressure ratio.
- Chart.js documentation - The charting library used for the curves.