Measurements made on a newly installed air-handling system...

Measurements made on a newly installed air-handling system were: $20 \mathrm{r} / \mathrm{s}$ fan speed, $2.4 \mathrm{~m}^3 / \mathrm{s}$ airflow rate, $340 \mathrm{~Pa}$ fan-discharge pressure, and $1.8 \mathrm{~kW}$ supplied to the motor. These measurements were made with an air temperature of $20^{\circ} \mathrm{C}$, and the motor. These measurements were math air at a temperature of $40^{\circ} \mathrm{C}$. If the fan speed remains at $20 \mathrm{r} / \mathrm{s}$, what will be the operating values of $(a)$ airflow rate, $(b)$ static pressure, and $(c)$ power? Ans. (c) $1.685 \mathrm{~kW}$ (GRAPH CANT COPY)

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Key Concepts

Fluid Density Effects

The density of the fluid (in this context, air) plays a critical role in fan performance. Changes in air temperature affect its density, which in turn influences the airflow rate, static pressure, and power consumption. A decrease in density, typically due to an increase in temperature, leads to lower static pressure and reduced power requirements for the same airflow if fan speed is held constant. This concept is essential when applying the affinity laws to predict performance under varying thermal conditions.

Fan Affinity Laws

The fan affinity laws relate the performance parameters of a fan—specifically, the airflow rate, static pressure, and power—to changes in operational conditions such as fan speed and fluid density. They provide mathematical relationships that allow predictions of how these parameters change when the fan operates under different conditions. For instance, airflow is directly proportional to the fan speed, static pressure is proportional to the square of the fan speed, and power consumption is generally proportional to the cube of the fan speed.