In the derivation of Thiem’s formula for steady radial flow to a well, which of the following assumptions is NOT applicable for an unconfined aquifer case?

Introduction / Context:
Thiem’s formula is widely used to analyze steady, laminar, radial groundwater flow to pumping wells. Correct identification of its modeling assumptions is critical to avoid applying it incorrectly.

Given Data / Assumptions:

• Steady state flow conditions around a well.
• Question asks which assumption is not applicable.
• Focus on well penetration, aquifer properties, and flow geometry.

Concept / Approach:
Thiem’s derivation for both confined and unconfined aquifers assumes that the pumping well fully penetrates the saturated thickness so that streamlines are essentially horizontal and radial, and vertical gradients are negligible.

Step-by-Step Solution:
List standard assumptions: homogeneous and isotropic aquifer; steady laminar flow; fully penetrating well; negligible well losses; radial and horizontal flow; small water surface slope for unconfined.Evaluate each option against these assumptions.The statement that the well is sunk only up to the water table (not fully penetrating) contradicts the fully penetrating assumption.Hence this statement is not applicable to the classical derivation.

Verification / Alternative check:
Texts show partial penetration induces vertical flow components and requires more complex solutions; classical Thiem flow net assumes full penetration.

Why Other Options Are Wrong:

• Homogeneous and isotropic: core assumption.
• Radial and horizontal flow: key simplification.
• Small water surface slope: used in unconfined analysis to linearize the drawdown surface.

Common Pitfalls:

• Using Thiem with partially penetrating wells without correction factors.
• Ignoring anisotropy which alters effective hydraulic conductivity.

Final Answer:
The well has been sunk only up to the water table surface and does not fully penetrate the aquifer