Density Ratio by Temperature and Altitude¶
Run the Density Ratio by Temperature and Altitude MicroSim Fullscreen
About This MicroSim¶
The chart plots the density ratio, actual air density divided by the standard-air density of 0.075 lb/ft³, against airstream temperature from 0°F to 1,000°F. There is one curve per site elevation, using the barometric pressures from the chapter's table (standard atmosphere):
| Elevation | Barometric pressure | Ratio at 70°F |
|---|---|---|
| 0 ft | 29.92 in. Hg | 1.000 |
| 2,500 ft | 27.31 in. Hg | 0.913 |
| 5,000 ft | 24.89 in. Hg | 0.832 |
| 7,500 ft | 22.65 in. Hg | 0.757 |
Every point follows the chapter's density ratio equation:
density ratio = (Pb ÷ 29.92) × (530 ÷ (T + 460)), and density = 0.075 × ratio
with T in °F and Pb in in. Hg. A dotted line at 1.000 marks standard air. The orange diamond is the temperature marker (0 to 1,000°F in 10°F steps) on the elevation you choose; the line under the chart gives its density ratio to three decimals, its density in lb/ft³ to four decimals, and the two factors that make it up. Hovering any curve shows the same values.
Five challenges follow, in this order:
| # | Question | Answer |
|---|---|---|
| 1 | Density ratio at 300°F, sea level? | 0.697 |
| 2 | Density ratio at 70°F, 5,000 ft? | 0.832 |
| 3 | Density ratio at 300°F, 5,000 ft? | 0.580 |
| 4 | Density ratio at 600°F, sea level? | 0.500 |
| 5 | A system needs 3.00 in. wg at 300°F, sea level. What standard-air pressure do you select from the catalog? | 4.30 in. wg |
A density ratio is correct within ±0.01 and a pressure within ±0.05 in. wg. You get two attempts. A wrong first answer shows the worked calculation; a second wrong answer shows the answer and counts the challenge as missed. While a challenge is open, the marker, the elevation list and the hover readouts are locked, so you calculate the value instead of reading it off the chart. When the challenge resolves, the chart marks its point on the right curve: a circle with ✓ for correct, a square with ✗ for missed. At the end the sim shows "n of 5 correct on first attempt" and the mastery line; mastery is 4 of 5 on the first attempt. Exploring the chart is never scored.
How to Use¶
- Move the Temperature marker and switch the Elevation. Check that the ratio at 600°F is exactly half the ratio at 70°F, and that each elevation curve is the sea-level curve multiplied by a constant (its barometric factor).
- Press Start challenges. Type each value in the answer box and press Check (or Enter). A correct answer reads "✓ Correct: value." in a solid green box; a wrong one reads "✗ Not quite." with the worked calculation in a dashed red box.
- Press Next challenge (or Enter). After challenge 5, press See score to read the first-attempt score, the mastery line and any missed challenges.
- The marker and hover readouts unlock again: confirm each marked point. Start over clears the marks and the score and returns to challenge 1.
Keyboard: Tab reaches the marker (arrow keys move it), the elevation list and every button. In the answer box, Enter checks; Enter again goes to the next challenge.
Data label: "Density ratio = (Pb ÷ 29.92) × (530 ÷ (T + 460)) · barometric pressures: Chapter 2 elevation table, standard atmosphere", 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/ch02-density-ratio-temperature-altitude/main.html"
height="882px"
width="100%"
scrolling="no"></iframe>
Lesson Plan¶
Learning Objective¶
The learner will calculate the air density ratio for a given airstream temperature and site elevation, to within ±0.01, and use it to convert a required pressure into a standard-air catalog pressure (Bloom: Apply, verb: calculate).
Audience¶
Adult professional development: new application engineers, sales staff, representatives and facilities staff who have read the "Barometric Pressure", "Standard Air" and "Hot Airstreams" sections of Chapter 2.
Duration¶
10-15 minutes
Prerequisites¶
- Standard air (0.075 lb/ft³, 70°F, 29.92 in. Hg)
- Barometric pressure and its fall with elevation
- Air density and the density ratio equation
- Hot airstreams, and the rule that pressure and power scale with the density ratio
Activities¶
- Explore (3 min): Read the ratio at 70°F, 300°F and 600°F on the sea-level curve; then switch to 5,000 ft and compare.
- Challenges (6-8 min): Work each challenge on paper first, writing the temperature in degrees Rankine (°F + 460).
- Review (2-3 min): Compare each marked point with your working. For challenge 5, say in words why the catalog pressure is higher than the job pressure.
Common Misconceptions Addressed¶
- Temperature in °F can be used without adding 460: challenges 1 and 4 and their feedback require 530 ÷ (T + 460); using 530 ÷ 300 gives a ratio above 1 that the chart shows cannot be right for hot air.
- Hot air raises the pressure a fan develops: every curve falls as temperature rises.
- To find the catalog pressure, multiply by the density ratio: challenge 5's feedback names 2.09 as the result of multiplying and explains that it would under-select the fan.
- Altitude and temperature corrections cannot be combined: challenge 3 multiplies the 0.832 barometric factor by the 0.697 temperature factor, and the 5,000 ft curve shows the product at every temperature.
Assessment¶
- At the end the sim shows "n of 5 correct on first attempt"; mastery is 4 of 5 on the first attempt. Moving the marker and hovering are exploration, not evidence.
- Follow-up question: a fan for a 400°F airstream at 2,500 ft draws 12.0 bhp on the catalog page. What does it draw in service at 400°F, and what does it draw on a cold start at 70°F? (0.913 × 530 ÷ 860 = 0.563, so 6.75 bhp hot; 0.913 × 12.0 = about 11.0 bhp cold at 2,500 ft.)
References¶
- Density of air - Wikipedia article on how air density depends on temperature and pressure, and on standard conditions.
- Barometric formula - Wikipedia article on how atmospheric pressure falls with altitude in the standard atmosphere.
- Standard conditions for temperature and pressure - Wikipedia article comparing reference conditions, including 70°F and 29.92 in. Hg.
- FanPedia: The Fan & Blower Encyclopedia - Twin City Fan's reference on fan performance at non-standard air densities and high-temperature construction.