51 Practice Exercises
Multiple Choice Questions
Exercise: Equipment Prices with the Effect of Capacity and Time
| Equipment Type | Range of Correlation | Capacity Units | Cost Exponent (n) |
|---|---|---|---|
| Air compressor, multiple stages | 1 -1500 | [latex]kW[/latex] | 0.85 |
| Shell and tube heat exchanger stainless steel | 1.9 – 1860 | [latex]m^2[/latex] | 0.60 |
| Horizontal tank carbon steel | 0.5-74 | [latex]m^3[/latex] | 0.30 |
| centrifugal pump stainless steel | 1-70 | [latex]hp[/latex] | 0.67 |
| Crystalizer | 0.2-3.8 | [latex]m^3[/latex] | 0.47 |
| Year | Marshall and Swift Equipment cost index | Chemical Engineering Plant Cost Index |
|---|---|---|
| 1996 | 211.7 | 154.7 |
| 2000 | 264.8 | 169.3 |
| 2004 | 301.7 | 186.3 |
| 2008 | 339.2 | 212.8 |
| 2012 | 391.5 | 227.8 |
| 2016 | 418.9 | 237.8 |
| 2020 | 458.3 | 258.8 |
In 2008, a carbon steel horizontal tank with a capacity of 26.5[latex]m^3[/latex] gallons costs $6700, then which of the following is the closest estimation to the cost of the same type of tank with a capacity of 50[latex]m^3[/latex] cost in 2020?
a)$9800
b)$10,100
c)$7,500
d)$8,000
Solution
b) $10,100
We combine the effect of capacity and time by multiplying the two factors. For time, we use the Marshall and Swift Equipment cost index because we are interested in the cost of a piece of equipment.
\begin{align*}
C_{2} &=C_{1}×\Big(\frac{A_{a}}{A_{b}}\Big)^n×\Big(\frac{I_{2}}{I_{1}}\Big)\\
C_{2} & = $6700×\Big(\frac{50}{26.5}\Big)^{0.30}×\Big(\frac{458.3}{339.2}\Big)\\
C_{2} & ≈ $10,100
\end{align*}
Exercise: Preliminary Estimation of Purchased Equipment Costs
Using the preliminary estimation of purchased equipment costs, estimate the price of a centrifugal compressor with the power of 400kW.
The value of a, b and n are shown as follows:
| Equipment | Units for Size, S | S lower | S upper | a | b | n |
| centrifugal compressors | driver power, kW | 75 | 30,000 | 490,000 | 16,800 | 0.6 |
a) $1,100,000
b) $7,210,000
c) $490,000
d) the size of the equipment is out of the range for effective estimation
Solution
a) $1,100,000
The size of the compressor is 400kW, which is within the range of S lower and S upper, so we can eliminate choice d).
Then we can use the formula:
\begin{align*}
C_e&=a+bS^n\\
&=490,000+16,800×(400)^{0.6}\\
&≈ $1,100,000
\end{align*}
Exercise: Calculating Depreciation
| Equipment A | Equipment B | |
| Purchased Value | $80,000 | $100,000 |
| Salvage Value | $30,000 | $40,000 |
| Life of Equipment | 5 years | 10 years |
Suppose we have 2 choices for a piece of equipment that serves the same purpose in our process, and we want to choose the equipment with the smallest depreciation, which one should we choose?
a) equipment A
b) equipment B
c) they have the same depreciation value
Solution
b) equipment B
\begin{align*}
&\text{Depreciation of equipment A}\\
&=\frac{\text{purchased value}-\text{salvage value}}{\text{life of equipment }(n)}\\
&=\frac{$80,000-$30,000}{5years}\\
&=$10000/year
\end{align*}
\b