Subtopic: Fluidization of granular solids – pneumatic, bucket, screw and belt conveying
Question Statement:
A bucket elevator has buckets of $2.5\text{ liters}$ capacity spaced $30\text{ cm}$ apart along a vertical belt moving at $1.8\text{ m/s}$. The bucket fill factor is $80\%$. If grain bulk density is $750\text{ kg/m}^3$, calculate the conveying capacity of the elevator in $\text{tonnes/h}$.
Answer Key:
32.4
Step-by-Step Solution & Explanation
Number of buckets discharging per second:
$n = \frac{v}{s} = \frac{1.8\text{ m/s}}{0.30\text{ m}} = 6\text{ buckets/s}$
Effective volume per bucket:
$V_e = 2.5\text{ L} \times 0.80 = 2.0\text{ L} = 0.002\text{ m}^3$
Volume per second:
$Q_v = 6 \times 0.002 = 0.012\text{ m}^3/\text{s}$
Mass flow rate:
$\dot{m} = 0.012\text{ m}^3/\text{s} \times 750\text{ kg/m}^3 = 9.0\text{ kg/s}$
In tonnes per hour:
$\text{Capacity} = \frac{9.0 \times 3600}{1000} = 32.4\text{ tonnes/h}$