Aquifer tests: If pumping from two wells at equal distance produces equal drawdown responses in an unconfined aquifer and a confined aquifer, the total thickness H of the confined aquifer is given by

Introduction / Context:
Interpreting pumping-test data often involves comparing water-table (unconfined) and confined aquifer responses. Equivalent drawdowns at equal radial distances can be used to relate saturated thickness and piezometric changes.

Given Data / Assumptions:

• Two observation wells located at equal distances from their respective pumped wells.
• Measured effects (drawdowns) are equal for the unconfined and confined cases.
• Symbols h1 and h2 denote corresponding head or thickness measures as per the setup (water table decline and piezometric decline).

Concept / Approach:
For unconfined aquifers, transmissivity depends on saturated thickness (~ proportional to head). For confined aquifers, transmissivity is constant with thickness H. Equating comparable responses (with appropriate linearized assumptions) leads to the relationship that the confined aquifer thickness equals the sum of the two representative head terms, giving H = h1 + h2.

Step-by-Step Solution:
Establish equal drawdown response s at equal r for both aquifers.Relate transmissivity in unconfined case to saturated thickness terms (h1, h2).For the confined case, transmissivity involves constant H.Balancing the influences yields H = h1 + h2.

Verification / Alternative check:
Linearized Dupuit-type assumptions for unconfined flow produce additive head-thickness terms; matching to confined flow recovers the sum relation for equivalent response.

Why Other Options Are Wrong:
Differences (h2 − h1 or h1 − h2) do not reflect the physics of transmissivity equivalence; parentheses in option (d) do not change the expression but represent the same as (c).

Common Pitfalls:
Confusing piezometric head drop with saturated thickness; ignoring that transmissivity varies with head in unconfined aquifers.

Final Answer:
H = h2 + h1.