Question

A 13 cm radius air duct is used to replenish the air of a room 9.2m x 5.8m x 4.4m every 19 min Part A How fast does air flow in the duct? Express your answer to two significant figures and include the appropriate units. li μΑ ? V = Value Units Submit Request Answer

Answer 1

The speed of air flow in the duct is 231.654 m/min.

Step-by-step explanation:

To calculate the speed of air flowing in the duct, we first need to calculate the volume of air that is replenished every 19 minutes. The volume of the room is given by its dimensions, which are 9.2m x 5.8m x 4.4m. Therefore, the volume of air in the room is 9.2m x 5.8m x 4.4m = 232.064m³. Since this volume needs to be replenished every 19 minutes, we can calculate the flow rate using the formula: flow rate = volume / time. The flow rate is 232.064m³ / 19 min = 12.212m³/min.

Now, we need to convert the flow rate to a velocity. Since the duct is circular, we can use the formula: velocity = flow rate / cross-sectional area. The cross-sectional area of the duct can be calculated using the formula for the area of a circle: area = π * radius². The radius of the air duct is given as 13 cm, which is equal to 0.13 m. Therefore, the cross-sectional area is π * 0.13² = 0.052825m². Finally, we can calculate the velocity by dividing the flow rate by the cross-sectional area: velocity = 12.212m³/min / 0.052825m² = 231.654 m/min.

Answer 2

The speed of air flow in the duct is 3.9 m/s when rounded to two significant figures after calculating the volume flow rate and the cross-sectional area of the duct.

Step-by-step explanation:

To determine the speed of air flow in the duct, we first need to calculate the volume of the room that is being replenished with air. We then calculate the volume flow rate, which is the volume per unit of time, and finally divide this flow rate by the cross-sectional area of the duct to find the speed of the air flow.

The volume of the room is found by multiplying the room's dimensions together:

• Volume = Length × Width × Height
• Volume = 9.2m × 5.8m × 4.4m = 235.216 m³

Now, to calculate the volume flow rate (Q), which is the volume that flows through the duct in a certain amount of time, we have:

• Q = Volume / Time
• Q = 235.216 m³ / 19 min
• To get the flow rate in seconds, we convert minutes into seconds (19 min × 60 seconds/min), so we have:
• Q = 235.216 m³ / 1140 seconds = 0.2065 m³/s

The cross-sectional area (A) of the duct is given by the formula A = πr², where r is the radius of the duct:

• A = π × (0.13m)² = 0.0531 m²

Finally, the speed of the air flow (v) in the duct can be calculated by dividing the flow rate by the cross-sectional area:

• v = Q / A
• v = 0.2065 m³/s / 0.0531 m² = 3.89 m/s

To two significant figures, the speed of air flow in the duct is 3.9 m/s, which is the appropriate answer.