Chapter 3, Problem 3.1P

To determine

The time required to complete the filling and emptying cycle for a refuse collection vehicle.

Answer to Problem 3.1P

The time required to complete the filling and emptying cycle for a refuse collection vehicle is $194.28\min$ .

Explanation of Solution

Given:

The two container of $80\text{gallons}$ each has $75\%$ full.

The refuse is picked up twice per week.

The truck has a compaction ratio of $1:2$ .

The pickup time is $1.58\min$ per service.

The time spend by truck on disposal is $20\min$ .

The time spend to reach the disposal site is $35\min$ .

Calculation:

Assume the volume of the truck as $20{\text{yd}}^{\text{3}}$ .

Calculate the volume of refuse produced by each resident in ${\text{yd}}^{\text{3}}$ .

  $\begin{array}{c}{V}_{\text{res}}=2\times 80\text{gallons}\times \left(\frac{0.00495{\text{yd}}^{\text{3}}}{1\text{gallon}}\right)\times 0.75\\ =0.594{\text{yd}}^{\text{3}}\end{array}$

Here, the volume of refuses produces by each resident is $V_{\text{res}}$ .

Write the expression to calculate the compacted volume by the truck’s compacting ratio.

  $V_{\text{com}}=\frac{1}{2}\times V_{\text{res}}$  ..... (I)

Here, the compacted volume is $V_{\text{com}}$ and the volume of refuse produced by each resident is $V_{\text{res}}$ .

Substitute $0.594{\text{yd}}^{\text{3}}$ for $V_{\text{res}}$ in Equation (I).

  $\begin{array}{c}{V}_{\text{com}}=\frac{1}{2}\times 0.594{\text{yd}}^{\text{3}}\\ =0.297{\text{yd}}^{\text{3}}\end{array}$

Write the expression to calculate the number of loads done by the truck.

  $L=\frac{V_{\text{truck}}}{V_{\text{com}}}$  ..... (II)

Here, the number of loads done by the truck is $L$ , the volume of the truck is $V_{\text{truck}}$ and the compacted volume is $V_{\text{com}}$ .

Substitute $20{\text{yd}}^{\text{3}}$ for $V_{\text{truck}}$ and $0.297{\text{yd}}^{\text{3}}$ for $V_{\text{com}}$ in Equation (II).

  $\begin{array}{c}L=\frac{20{\text{yd}}^{\text{3}}}{0.297{\text{yd}}^{\text{3}}}\\ =67.34\\ \approx 68\end{array}$

Write the expression to calculate the total time of cycle.

  $T_{\text{C}}=2\times T_{\text{d}}+\left(T_{\text{s}}\times L\right)+T_{\text{dis}}$  ..... (III)

Here, the total time of cycle is $T_{\text{C}}$ , the time spend to reach the disposal site is $T_{\text{d}}$ , the number of loads done by the truck is $L$ , the service time is $T_{\text{s}}$ and the time spend by truck on disposal is $T_{\text{dis}}$ .

Substitute $35\min$ for $T_{\text{d}}$ , $1.58\min$ for $T_{\text{s}}$ , $68$ for $L$ and $20\min$ for $T_{\text{dis}}$ in Equation (III).

  $\begin{array}{c}{T}_{\text{C}}=2\times 35\min +\left(1.58\min \times 66\right)+20\min \\ =70\text{min}+104.28\text{min}+20\min \\ =194.28\min \end{array}$

Conclusion:

Thus, the time required to complete the filling and emptying cycle for a refuse collection vehicle is $194.28\min$ .