Chapter 2, Problem 2.1P

To determine

The time after which the town will require a new landfill.

Answer to Problem 2.1P

The time after which town will require a new landfill is $84.16\text{days}$ .

Explanation of Solution

Given:

The population is $20000$ .

The industrial waste produced is $1000\text{tons}$ .

The estimated life of landfill is $10\text{years}$ .

Concept used:

Write the expression to calculate the amount of waste generated by the residents per day.

  $W_{\text{R}}=w\times P$   ..... (I)

Here, waste generated per capita per day is $w$ , amount of waste generated by the residents per day is $W_{\text{R}},$ and the population of total resident is $P$ .

Write the expression to calculate the capacity of landfill.

  $C=W_{\text{R}}\times n$   ..... (II)

Here, the capacity of landfill is $C$ and estimated life of landfill is $n$ .

Write the expression for total waste generated per day.

  $W_T=W_{\text{R}}+W_{\text{I}}$   ..... (III)

Here, the total waste generated per day is $W_{\text{T}}$ , the amount of industrial waste generated per day is $W_{\text{I}}$ .

Write the expression for life of landfill.

  $N=\frac{C}{W_{\text{T}}}$   ..... (IV)

Calculations:

Assume the waste generation rate per-capita is $2.36\text{lb}/\text{capita}/\text{day}$ and the industrial waste generation rate is $1000\text{tons}/\text{day}$ .

Calculate the amount of waste generated by the resident per day.

Substitute $2.36\text{lb}/\text{capita}/\text{day}$ for $w$ and $20000$ for $P$ in Equation (I).

  $\begin{array}{c}{W}_{\text{R}}=2.36\text{lb}/\text{capita}/\text{day}\times 20000\\ =47200\text{lb}/\text{day}\left(\frac{1\text{tons}}{2000\text{lb}}\right)\\ =23.6\text{tons}/\text{day}\end{array}$

Calculate the capacity of landfill.

Substitute $23.6\text{tons}/\text{day}$ for $W_{\text{R}}$ and $10\text{years}$ for $n$ in Equation (II).

  $\begin{array}{c}C=23.6\text{tons}/\text{day}\times 10\text{years}\left(\frac{365\text{days}}{1\text{year}}\right)\\ =86140\text{tons}\end{array}$

Calculate the total waste generated per day.

Substitute $23.6\text{tons}/\text{day}$ for $W_{\text{R}}$ and $1000\text{tons}/\text{day}$ for $W_{\text{I}}$ in Equation (III).

  $\begin{array}{c}{W}_T=23.6\text{tons}/\text{day}+1000\text{tons}/\text{day}\\ =1023.6\text{tons}/\text{day}\end{array}$

Calculate the life of the landfill.

Substitute $86140\text{tons}$ for $C$ and $1023.6\text{tons}/\text{day}$ for $W_{\text{T}}$ in Equation (IV).

  $\begin{array}{c}N=\frac{86140\text{tons}}{1023.6\text{tons}/\text{day}}\\ =84.16\text{days}\end{array}$

Conclusion:

Thus, the time after which town will require a new landfill is $84.16\text{days}$ .