"When a revolutionary succeeds, he should be given five years then shot, or otherwise removed."

## Introduction

I was so happy with my previous fan installation that I am considering replacing some old fans with new, higher throughput, and quieter fans. The installations will be similar to that shown in Figure 1.

I have been using a nomograph (Figure 2) for my home HVAC calculations (example). I have decided that I am now living in the 21st century and I should figure out the formula that this graph represents. In this post, I will generate part of this nomograph to verify that I have put together the correct formula.

## Background

Figure 2 shows the nomograph that I want to calculate for myself using the Darcy-Weisbach formula.

The chart makes certain assumptions.

- 100 foot duct length
- Fixed temperature, altitude, and humidity values that are unstated
- No duct roughness factor stated

I will make some reasonable guesses and compute my version of the nomograph.

## Analysis

I wanted a formula that would allow me to change the temperature, humidity, and air density. Figure 1 shows my calculation setup and how I determined the Reynolds number of the air. The model in Figure 1 for air density and specific humidity is rough. I show an alternative form in Appendix A that appears to be a bit more accurate. It does not make a huge difference in my final result.

Now that I have the Reynolds number, I can compute the Darcy friction factor and define my Darcy-Weisbach formula (Figure 4).

Now that I have my flow volume and velocity formulas defined, I can plot them (Figure 6) in the same manner as Figure 2. I did not plot every case shown in Figure 2 because it would take too long. However, I am quite confident that I have a formula that is close to the same one that was used to compute the graph in Figure 2.

## Conclusion

I now have a formula that I can use in place of the graph shown in Figure 2. This will be more convenient for me in the analysis work that I have coming up.

## Appendix A: Alternative Approach for Computing the Density and Specific Humidity of Moist Air

I worked the moist air density and specific humidity problems a couple of ways and this is one alternative (Figure 7) that I investigated. They do not give exactly the same answers, but the results are similar.

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Dear Mark, I enjoy, although not being an engineer, your blog quite a lot. I have a question with respect to your calculation in figure 3. What is the origin of these formulas (the link to engineer's toolbox does not work)

Thanks for your help

First, I am glad you enjoy the blog. I actually am shocked at the number of people who read it because the blog started just as a searchable place to put my engineering notes (I hate notebooks). Second, I am very glad that you wrote me when something doesn't work – I try to fix those things immediately. Both links now work.

Please read the discussion on the Engineering Toolbox about these formulas. If they are still not clear after reading their discussion, write me another question.

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