Question

A typical ceiling fan running at high speed has an airflow of about 1.85 ✕ 10^3 ft^3/min, meaning that about 1.85 ✕ 10^3 cubic feet of air move over the fan blades each minute.

Determine the fan's airflow in m^3/s.

Answer 1

To convert the given airflow of 1.85 × 10³ ft³/min to m³/s, we apply conversion factors for feet to meters and minutes to seconds, yielding an airflow of approximately 0.873 m³/s.

Step-by-step explanation:

To determine the fan's airflow in cubic meters per second (m3/s), we need to convert the given airflow from cubic feet per minute (ft3/min) to m3/s. The conversion factors needed are 1 ft = 0.3048 m and 1 min = 60 s. To convert 1.85 × 103 ft3/min to m3/s:

• First, convert cubic feet to cubic meters: 1.85 × 103 ft3 × (0.3048 m/1 ft)3 = 52.37 m3/min.
• Then, convert minutes to seconds: 52.37 m3/min × (1 min/60 s) = 0.873 m3/s.

Therefore, the fan's airflow in m3/s is approximately 0.873 m3/s.

Answer 2

0.83 m³/s

Step-by-step explanation:

The speed of the airflow is given as;

1.85 x 10³ ft³/min

Now we are to express this unit in m³/s

1ft = 0.3m

60s = 1 min

So;

1.85 x 10³ x ft³ x
`(1)/(min)` x
`((0.3m)^(3) )/(ft^(3) )` x
`(1min)/(60s)`

= 0.83 m³/s