A 19cm radius air duct is used to replenish the air of a room 9.2m x 6.0m x 4.0m every 18min . How fast does air flow in the duct?

Use the equation Area = Volume / (velocity)x(time)

Rearrange the equation to solve for velocity.

So, (9.2x6.0x4.0) /
(Pi)(0.19)^2(1080)

So, the answer is 1.8m/s

To find out how fast air flows in the duct, we need to calculate the volumetric flow rate.

1. Find the volume of the room:
Volume of the room = Length x Width x Height
Volume of the room = 9.2m x 6.0m x 4.0m
Volume of the room = 220.8 cubic meters

2. Determine the time required to replenish the air in the room:
Time required = 18 minutes

3. Calculate the volumetric flow rate:
Volumetric flow rate = Volume of the room / Time required
Volumetric flow rate = 220.8 cubic meters / 18 minutes
Volumetric flow rate = 12.27 cubic meters per minute

4. The air duct has a radius of 19 cm, which is equivalent to 0.19 meters.
We can calculate the cross-sectional area of the duct using the formula:
Area = π x radius^2
Area = π x (0.19)^2
Area ≈ 0.1131 square meters

5. Finally, we can calculate the air velocity in the duct:
Air velocity = Volumetric flow rate / Cross-sectional area of the duct
Air velocity = 12.27 cubic meters per minute / 0.1131 square meters
Air velocity ≈ 108.47 meters per minute

Therefore, the air flows at a speed of approximately 108.47 meters per minute in the duct.

To determine the speed of air flow in the duct, we need to use the formula:

Flow rate (Q) = Velocity (v) * Cross-sectional Area (A)

We are given the radius of the air duct as 19cm, so the diameter of the duct is 38cm or 0.38m (2 * radius).

Now, to find the cross-sectional area (A) of the duct, we can use the formula:

A = π * r^2

where r is the radius of the duct.

A = π * (0.19m)^2
A ≈ 0.113 m^2

Next, we need to find the flow rate (Q) of the air in the room. We know that the room is 9.2m long, 6.0m wide, and 4.0m high. The total volume of the room can be calculated as:

Volume = Length * Width * Height
Volume = 9.2m * 6.0m * 4.0m
Volume = 220.8 m^3

The air needs to be replenished every 18 minutes. Therefore, the flow rate (Q) can be calculated as:

Q = Volume / Time
Q = 220.8 m^3 / 18 min
Q ≈ 12.27 m^3/min

Finally, we can use the formula mentioned earlier to find the velocity (v) of the air flow:

Q = v * A
v = Q / A
v = 12.27 m^3/min / 0.113 m^2
v ≈ 108.36 m/min

Therefore, the air flows at a speed of approximately 108.36 meters per minute in the duct.