Final answer:
The purpose of a heating duct is to heat the air as part of a forced air gas heater system, ensuring comfortable temperatures within a home. It is not primarily for cooling, filtering, or humidifying the air, although filtering can be a secondary function. To find the air speed in the duct, calculate the house's volume, find the flow rate, and then use the duct's cross-sectional area.
Step-by-step explanation:
The purpose of a heating duct is to warm the incoming air before it is distributed into a space. Specifically, in the scenario provided, the heating duct is part of a forced air gas heater system designed to circulate air.
The function of this heating system is to maintain a comfortable temperature within the home by transferring heat to the circulating air. This process is known as convection and can be an efficient method for heating a home.
Filters in these systems also help to filter the air, but that is not the primary purpose being addressed by this question.
To calculate the average speed of air in the duct, first, we need to determine the volume of the house that the air duct system is sustaining. The volume of the house is equivalent to a rectangular solid with the given dimensions, which would be 13.0 m (width) × 20.0 m (length) × 2.75 m (height).
Then we divide this volume by the time it takes for the air to be cycled through the house to find the flow rate.
Lastly, we use the cross-sectional area of the duct and the flow rate to calculate the average air speed within it.