Question

Equipment costs generally follow the relation:

• A. Linear with size
• B. Power law with size
• C. Exponential with size
• D. Inversely with size

Hint:

Remember the six-tenths rule: cost of equipment scales as size$^{0.6}$ for rough estimates. This is a power law and reflects real-world scaling effects.

Answer 1

The Correct Option is B

In engineering economics and cost estimation, the cost of equipment does not increase linearly with size.
Instead, it typically follows a power law relationship, which can be mathematically expressed as:
\[ C_2 = C_1 \left( \frac{S_2}{S_1} \right)^n \]
Where:
- $C_1$, $C_2$ are the costs of equipment at sizes $S_1$ and $S_2$ respectively
- $n$ is the scaling exponent, typically between 0.6 and 0.8 for most industrial equipment
This rule is known as the six-tenths rule when $n = 0.6$, commonly used in preliminary cost estimation.
The implication is that as the size or capacity of equipment increases, the cost increases, but at a rate lower than linear — reflecting economies of scale.
Let’s briefly consider the incorrect options:
- (1) Linear with size: This would suggest cost doubles when size doubles, which is generally not true in engineering equipment due to fixed costs and scaling effects.
- (3) Exponential with size: Exponential growth would imply costs rise much faster than size — unrealistic for engineering cost behavior.
- (4) Inversely with size: This is incorrect; cost does not decrease as size increases.
Hence, the most accurate model is the power law relation.