Fan Airflow Versus Static Pressure Diagram

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

Introduction

Figure 1: Typical Bathroom Ventilation Scenario.

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.

Figure 2: Air Flow Versus Static Pressure Drop.

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.

Figure 3: Calculation Setup and Reynolds Number Determination.

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

Figure 4: Creation of Functions for Graphing.

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.

Figure 6: Generate My Version of 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.

Figure 7: Alternative Approach for Computing Density and Specific Humidity of Moist Air.