Question

In a longwall face, the full seam thickness of 3 m is cut by a shearer with a web depth of 0.7 m. Hauling speed = 12 m/min. AFC trough cross-section = 0.4 m$^2$, loading coefficient = 0.7. Find the AFC speed (in m/s), rounded to one decimal place.

Hint:

AFC speed is discharge per second divided by effective trough area. Loading coefficient must always be included.

Answer 1

Correct Answer: 1.4

Step 1: Coal production rate by the shearer. Volume cut per minute: \[ Q_v = (\text{seam thickness}) \times (\text{web depth}) \times (\text{shearer speed}) \] \[ Q_v = 3 \times 0.7 \times 12 = 25.2\ \text{m}^3/\text{min} \] Convert to m$^3$/s: \[ Q_v = \frac{25.2}{60} = 0.42\ \text{m}^3/\text{s} \] --- Step 2: AFC carrying capacity. Effective area: \[ A_{\text{eff}} = 0.4 \times 0.7 = 0.28\ \text{m}^2 \] AFC velocity: \[ v_{\text{AFC}} = \frac{Q_v}{A_{\text{eff}}} = \frac{0.42}{0.28} = 1.50\ \text{m/s} \] Rounded to one decimal: \[ \boxed{1.5\ \text{m/s}} \]