Economical Lining and Benefit-Cost Ratio

The concept of the benefit-cost ratio (BCR) is widely used in engineering economics to evaluate the economic viability of a project or a component like a lining. It compares the total benefits expected from an investment to the total costs incurred.

The formula for the benefit-cost ratio is:

$\text{Benefit-Cost Ratio} = \frac{\text{Total Benefits}}{\text{Total Costs}}$

Let's analyze what different values of the benefit-cost ratio signify:

• Benefit-Cost Ratio > 1: This means the total benefits outweigh the total costs. The project or investment is generally considered economically attractive or profitable.
• Benefit-Cost Ratio = 1: This means the total benefits are exactly equal to the total costs. This represents the break-even point, where the investment is justified by the benefits it provides, but there is no net profit beyond recovering the costs.
• Benefit-Cost Ratio < 1: This means the total costs exceed the total benefits. The project or investment is generally considered uneconomical or not financially justified.

The question asks for the "most economical type of lining". In this context, a lining is considered economical if the benefits it provides (e.g., reducing water loss, increasing flow efficiency, reducing maintenance) are commensurate with its cost.

While a benefit-cost ratio > 1 indicates a profitable investment, the ratio that signifies the most economical *type* of lining in terms of justification of costs by benefits is often considered to be where the benefits precisely balance the costs. This is represented by a benefit-cost ratio equal to 1.

Let's consider the given options:

• Maximum benefit - cost ratio: This represents maximum profitability, not necessarily the condition for the most economical *type* in the sense of just justifying the cost.
• Zero benefit - cost ratio: This implies zero benefits, which is clearly not economical as costs are incurred without any return.
• Benefit - cost ratio = 1: This represents the point where benefits equal costs, making the lining investment exactly justifiable on economic grounds. It is the threshold of economic viability.
• Minimum benefit - cost ratio: This would likely be a ratio less than 1, indicating costs exceed benefits, which is uneconomical.

Therefore, a benefit-cost ratio of 1 is typically considered the condition for the most economical type of lining, as it signifies that the benefits derived are exactly equal to the cost incurred, representing a balanced economic justification.