The performance data of Problem 10.84 are for a...

The performance data of Problem 10.84 are for a 36-in.-diameter fan wheel. The fan also is manufactured with $42-, 48-, 54-,$ and 60 -in. diameter wheels. Pick a standard fan to deliver $600 \mathrm{ft}^{3} / \mathrm{s}$ against a $1-\mathrm{in.} \mathrm{H}_{2} \mathrm{O}$ static pressure rise. Determine the required fan speed and input power required.

Key Concepts

Fan Selection Criteria

Fan selection involves matching the design requirements—such as a given flow rate and static pressure rise—with the available standard fan sizes. This process relies on using scaling relationships and performance curves to ensure that the selected fan, among the various standard sizes, can deliver the needed performance efficiently while considering the implications on fan speed and power consumption.

Power Consumption Scaling

Understanding how power consumption scales with fan size and speed is crucial for energy considerations and motor selection. Through the affinity laws, it is established that the power demand increases dramatically with increases in diameter and rotational speed, which is important when calculating the input power required to meet specified performance conditions.

Fan Affinity Laws

The fan affinity laws provide the fundamental scaling relationships that relate the fan’s flow rate, static pressure, and power consumption to its rotational speed and diameter. According to these laws, the flow rate is proportional to the rotational speed and the cube of the fan diameter, the static pressure is proportional to the square of both the speed and the diameter, and the power is proportional to the cube of the speed and roughly the fifth power of the diameter. These relationships allow for performance predictions when scaling the operation of geometrically similar fans.

Dimensional Analysis for Scaling

Dimensional analysis is used to develop non-dimensional parameters that relate the performance of geometrically similar devices, such as fans, across different sizes. This approach helps in scaling performance data from one fan size to another by maintaining the same dimensionless groups, thus ensuring that the flow characteristics and efficiency are preserved despite size changes.

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