Seeking advice on calculating the shaft power of a fan
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I have a question regarding the calculation of the shaft power of a fan that I haven’t been able to resolve; please explain it to me. Conditions: Assume that there is a cooler installed behind a boiler, and it is of the air-cooled type, with no outside air leaking in. The boiler outlet temperature is 473°C, the negative pressure is -1000 Pa, and the resistance of the cooler is also 1000 Pa. The cooler outlet temperature is 100°C. Assuming that the air flow rate at the cooler outlet is 10,000 m3/h, the air flow rate at the boiler outlet is approximately 20,000 m3/h. (Here, only temperature is considered, and the effect of pressure on the airflow under operating conditions is not taken into account.) Question: If the fan is placed behind the cooler, then the shaft power 1 = 10000*2000/fan efficiency. If the fan is placed behind the boiler, then the shaft power 2 = 20000*2000/fan efficiency. (When the fan is placed behind the boiler, since the cooler operates under positive pressure, the resistance may be less than 1000 Pa, but it isn’t much lower either; therefore, 1000 Pa is also assumed.) Shaft power 2 = Shaft power 1 * 2; since the wind energy losses in the cooler and boiler remain constant, shaft power 2 should be equal to or similar to shaft power 1. Why is the shaft power 2 = shaft power 1 * 2? ? ? ? The formula for shaft power is independent of temperature and density; it depends only on the airflow volume, pressure under operating conditions, and the efficiency of the fan. So where is the problem?
Although the formula for shaft power is independent of temperature and density, the flow rate and pressure of the medium are highly dependent on temperature and density. The numbers you mentioned above are hypothetical; if you calculate them yourself, the results will differ significantly from your estimates.
Thank you for your reply, but you didn’t understand the real meaning of my question, nor did you provide any valuable information. Whether the power of the two is twice as much or not, even a significant difference can address my question. The power consumption of the boiler and cooler remains unchanged; however, depending on the location where the fans that provide power are placed, the calculated shaft power values can vary significantly, which is not consistent with the principles of energy conservation.
Since you’re concerned about energy conservation, let’s first determine which system it is