# Constant Volume Fans

I had a little problem at work where a process was behaving differently in the summer and in the winter. No obvious explanation was available. One thing that did change significantly in the summer and winter was the suction of the ventilation system. Unfortunately, the depression measurements in place weren’t particularly accurate, so I started to wonder what is the potential change in ventilation based on various assumptions concerning air temperature and humidity while using a constant volume fan. In the end, the difference in ventilation didn’t appear to have a significant influence – but it was something that was interesting at the time and may prove useful to consider at a later date.

So here’s the problem, consider that you have a fan that can pull a constant volume. In the summer it’s dealing with air which is at a minimum of 30 degrees centigrade. During the winter the temperature is closer to 10 degrees centigrade. Now since we’re always dealing with the same volume – all that we’re really interested in isĀ  the difference in air density as a function of temperature and humidity.

The following is a table showing the effect of temperature and relative humidity on air density at atmospheric pressure (101325 Pa). The densities were calculated from the ideal gas law – considering a mixture of air (molar mass of 28.9645 g/mol) and water (molar mass of 18.01528 g/mol). The saturation vapour pressure of water was obtained from wikipedia – citing the CRC Handbook of Chemistry and Physics published in 2005. I don’t have my copy of the handbook on me so I couldn’t validate that the values were correctly transcribed.

We can now perform a quick calculation depending on relative humidity. If we consider the simple case of 90 percent humidity – we have a 8.16% increase in density (a relatively significant change in volume is pulled) between 30 and 10 degrees centigrade.

 Temperature Humidity K C 0 10 20 30 40 50 60 70 80 90 100 273 0 1.29 1.29 1.29 1.29 1.29 1.29 1.29 1.29 1.29 1.29 0.80 283 10 1.25 1.25 1.25 1.24 1.24 1.24 1.24 1.24 1.24 1.24 0.78 293 20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.20 1.19 0.75 303 30 1.16 1.16 1.16 1.16 1.16 1.16 1.15 1.15 1.15 1.15 0.72 313 40 1.13 1.12 1.12 1.12 1.11 1.11 1.11 1.11 1.10 1.10 0.70 323 50 1.09 1.09 1.08 1.08 1.07 1.07 1.06 1.06 1.05 1.05 0.68 333 60 1.06 1.05 1.04 1.04 1.03 1.02 1.01 1.00 1.00 0.99 0.66 343 70 1.03 1.02 1.00 0.99 0.98 0.97 0.96 0.94 0.93 0.92 0.64 353 80 1.00 0.98 0.96 0.95 0.93 0.91 0.89 0.88 0.86 0.84 0.62 363 90 0.97 0.95 0.92 0.90 0.87 0.84 0.82 0.79 0.77 0.74 0.60 373 100 0.95 0.91 0.87 0.84 0.80 0.77 0.73 0.70 0.66 0.62 0.59