In dam economics, the “economic height” is the height at which which criterion is satisfied?

Introduction:
Selecting dam height balances incremental construction cost against incremental storage benefit. The “economic height” is the result of optimizing this balance for minimum cost per unit of useful storage.

Given Data / Assumptions:

• Cost rises with height due to larger structures and appurtenances.
• Storage also rises with height, but with diminishing returns at higher elevations.

Concept / Approach:
Define unit storage cost C_u = Total cost / Live storage. The economic height occurs at the minimum of C_u with respect to height, where marginal cost per extra unit storage equals the average cost per unit storage.

Step-by-Step Solution:
Relate cost curve (increasing, convex) and storage curve (increasing, concave). Compute/visualize C_u vs. height; identify its minimum. Interpret this minimum as the economic height because it yields the cheapest storage per unit volume.

Verification / Alternative check:
Benefit–cost analysis similarly points to the height where additional storage no longer justifies its extra cost, aligning with the minimum of C_u.

Why Other Options Are Wrong:

• Least silting/freeboard: Operational/safety constraints, not the economic optimum definition.
• Maximum unit cost: Opposite of optimization goal.
• None of these: Incorrect as the definition is standard.

Common Pitfalls:

• Confusing economic height with safe hydraulic height (flood routing and freeboard).
• Optimizing total cost rather than unit storage cost.

Final Answer:
Cost of the dam per unit of storage is minimum.