Question

In an underground coal mine, a fan delivers air through a cross-sectional area of \(5~\mathrm{m^2}\) with an average air velocity of \(4~\mathrm{m/s}\). What is the quantity of air circulated by the fan?

• A. \(15~\mathrm{m^3/s}\)
• B. \(20~\mathrm{m^3/s}\)
• C. \(20~\mathrm{m^3/min}\)
• D. \(15~\mathrm{m^3/min}\)

Hint:

The air quantity in a mine airway is \[ \boxed{Q=A\times V,} \] where \(A\) is the cross-sectional area and \(V\) is the average air velocity.

Answer 1

The Correct Option is B

Step 1: Use the discharge equation. The quantity of air is \[ Q=AV, \] where \[ A=5~\mathrm{m^2}, \qquad V=4~\mathrm{m/s}. \]

Step 2: Calculate the quantity of air. \[ Q=5\times4=20~\mathrm{m^3/s}. \] Hence, \[ \boxed{20~\mathrm{m^3/s}} \] is the correct answer. Therefore, \[ \boxed{(B)} \] is the correct answer.