Density Correction Calculator¶
Run the Density Correction Calculator MicroSim Fullscreen
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About This MicroSim¶
Catalog ratings assume standard air (0.075 lb/ft³ at 70°F and sea level). This calculator practices the density corrections from the section "Density Corrections" in Chapter 10:
- Temperature factor: Kt = 530 ÷ (T + 460), with T in °F
- Altitude factor: Ka = (1 − 6.875 × 10⁻⁶ × h)^5.2559, with h in feet
- Combined factor: Kd = Kt × Ka
- Standard-air pressure for catalog selection = actual pressure ÷ Kd
- Actual BHP = catalog BHP × Kd
The sim starts with three challenge jobs, in this fixed order (illustrative values; job 3 is the chapter's worked example "A Hot Fan at Altitude"):
| # | Job | Asked | Model answer |
|---|---|---|---|
| 1 | 200°F air at sea level (0 ft) | Combined factor | 0.803 |
| 2 | 70°F air at 5,000 ft | Combined factor | 0.832 |
| 3 | 200°F air at 5,000 ft, 3.0 in. wg actual static pressure, 10,000 CFM | Combined factor, then standard-air pressure | 0.668, then 4.49 in. wg |
A factor is correct within ±0.01 of the model value and a pressure within ±0.05 in. wg. Every answer gets two attempts; after the second wrong attempt the model value is shown and the answer counts as missed. Job 3 has two parts: the pressure question appears only after the factor is checked, and the job counts as correct only when both parts are. Two common slips get an extra line: a job-1 factor near 70 ÷ 200 = 0.35 ("Add 460 to each temperature first.") and a job-3 pressure near 3.0 × 0.668 = 2.00 ("That multiplies by the factor; to enter a standard-air catalog, divide by it."). After each answer the sim shows the model value and the one-line calculation, and the factor chain Kt × Ka = Kd on the right fills in.
Mastery is 3 of 3 jobs fully correct on the first attempt. After job 3, Explore mode unlocks four sliders: air temperature (0 to 800°F), site elevation (0 to 10,000 ft), actual static pressure (0.5 to 15.0 in. wg) and catalog BHP at the standard-air point (1.0 to 200.0 BHP). The three factors, the standard-air pressure and the actual BHP update at once. Explore mode is never scored.
How to Use¶
- Read job 1, type the combined factor in Your answer and press Check (or Enter).
- A correct answer reads "✓ Correct: model value." in a solid green box. A wrong one reads "✗ Not quite." with the calculation hint in a dashed red box; use the second attempt.
- Press Next challenge (or Enter) for job 2, then job 3: type the factor, press Next: part 2, and type the standard-air pressure. "Challenges correct: n of 3" keeps the running score.
- After job 3, press Start exploring. Set 800°F at sea level and see the combined factor fall to 0.421, so the catalog pressure is more than twice the job pressure. Set 200°F, 5,000 ft, 3.0 in. wg and 11.0 BHP to see the chapter's dryer example: 4.49 in. wg in, 7.35 BHP out. Start over clears the score and returns to job 1.
Keyboard: Enter checks the answer, and Enter again goes to the next part or job. Tab reaches the answer box, every button and the four sliders; the arrow keys move a focused slider.
Data label: "Illustrative values · standard air 0.075 lb/ft³ at 70°F, sea level", 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/ch10-density-correction-calculator/main.html"
height="642px"
width="100%"
scrolling="no"></iframe>
Lesson Plan¶
Learning Objective¶
The learner will calculate the combined density correction factor for a stated air temperature and site elevation, and use it to convert an actual static pressure to the standard-air pressure used for catalog selection, to within ±0.01 on the factor and ±0.05 in. wg on the pressure (Bloom: Apply, verb: calculate).
Audience¶
Adult professional development: new application engineers, sales staff, representatives and facilities staff who have read the section "Density Corrections" in Chapter 10.
Duration¶
10-15 minutes
Prerequisites¶
- Standard air and the density correction factor
- Temperature correction and degrees Rankine (°F + 460)
- Altitude correction
Activities¶
- Challenges (5-8 min): Work each job with a calculator before pressing Check. Write Kt and Ka separately, then multiply.
- Review (2 min): For job 3, say aloud which way each value goes: pressure into the catalog is divided by Kd; horsepower out of the catalog is multiplied by Kd.
- Explore (3-5 min): Find the temperature at which the catalog pressure is half again the job pressure at sea level (Kd about 0.667, near 335°F), then add elevation and watch it grow.
Common Misconceptions Addressed¶
- The fan moves less CFM in hot or thin air at the same speed: the sim repeats that airflow volume is the same at any density for a fan at fixed speed.
- The actual pressure is multiplied by the factor to get the catalog pressure: a job-3 answer near 2.00 in. wg gets the "divide by it" correction.
- Temperature in °F can be used directly in the ratio: a job-1 answer near 0.35 gets the "add 460" correction.
Assessment¶
- The running line "Challenges correct: n of 3" counts jobs solved on either attempt. At the end the sim shows "First-attempt score: n of 3" and the mastery line; mastery is 3 of 3 jobs fully correct on the first attempt.
- Moving the sliders in Explore mode is not evidence of mastery. Ask the learner why a hot fan needs a cold-start motor check.
References¶
- Density of air - Wikipedia article on how air density varies with temperature and pressure.
- Barometric formula - Wikipedia article on the standard-atmosphere pressure change with altitude behind the altitude factor.
- FanPedia: The Fan & Blower Encyclopedia - Twin City Fan's reference on fan ratings at standard air and corrections for temperature and altitude.