Mr Tan is engaging a contractor to install large ceiling fans in the school hall. The hall is a large rectangular space, \(30\) metres long, \(20\) metres wide and \(8\) metres high.
There are two requirements: (1) Good air circulation—the fans together must meet the minimum airflow requirement. (2) Comfortable cooling environment—each fan must produce an air velocity of at least \(0.3\text{ m/s}\).
The vendor provides these formulas: volume of air moved by a fan for 1 full rotation, \(VFR=\) circular cross-sectional area of the fan \(\times\) height of air column; volume moved per second, \(VPS=VFR\times RPM\div60\); minimum airflow requirement in \(\text{m}^3/\text{min}=\) total volume of school hall \(\div5\); total airflow generated per minute in \(\text{m}^3/\text{min}=VFR\times70\times\) number of fans; air velocity \(=VPS\div\) circular cross-sectional area of the fan.
The vendor also provided the specifications of three fan models.
| Type | Blade length (m) | Number of blades | Motor Power (W) | Height of air column (m) | Full rotations per minute (RPM) | Weight (kg) |
|---|---|---|---|---|---|---|
| \(A\) | \(2.0\) | \(5\) | \(75\) | \(0.5\) | \(60\) | \(32.0\) |
| \(B\) | \(2.5\) | \(5\) | \(90\) | \(0.5\) | \(50\) | \(35.0\) |
| \(C\) | \(3.0\) | \(6\) | \(120\) | \(0.6\) | \(45\) | \(38.0\) |
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