Final answer:
Ductwork must be large enough to handle the required volume of air for proper air conditioning operation. By calculating the air volume that needs to circulate within a given timeframe and the cross-sectional area of the duct, one can determine the average speed of the air necessary for optimal system performance.
Step-by-step explanation:
The ductwork in an air conditioning (A/C) system should be large enough to handle the volume of air needed for correct operation. To determine the appropriate size, we need to abide by the principles of fluid dynamics and consider the airflow requirements of the system. Let's calculate the average speed of the air in the duct using a given scenario.
The volume of the house is given by the product of its width, length, and height: 13.0 m × 20.0 m × 2.75 m. The resulting volume is the amount of air that needs to be circulated. With the main uptake air duct being 0.300 m in diameter, we can determine the cross-sectional area of the duct (πr²). Then, knowing the volume of air (the house's interior volume) and the time frame (every 15 minutes), we can find the average airspeed in the duct by calculating the volume flow rate (volume/time) and combining it with the cross-sectional area of the duct.
For example, if the house's interior volume is to be replaced every 15 minutes, and the duct has a diameter of 0.300 m, the appropriate average speed of airflow can be determined to ensure proper system performance. In practice, the speed should be such that it allows the entire air volume to circulate within the given time without causing excessive noise or strain on the A/C system.
Air flowrate, duct sizing, and AC operation are key considerations when designing a heating, ventilation, and air conditioning (HVAC) system. An undersized duct could lead to inadequate airflow and an overheated system, while an oversized duct may result in unnecessary energy consumption and installation costs.