Dupuit–Thiem steady radial flow to wells: The derivation of Thiem’s formula relies on which set of assumptions?

Introduction / Context:
Thiem’s equations provide steady-state discharge–drawdown relations for wells in confined and unconfined aquifers. The classical derivation uses the Dupuit assumptions to simplify three-dimensional flow to a tractable form.

Given Data / Assumptions:

• Homogeneous, isotropic aquifer media.
• Full-penetration well without partial penetration effects.
• Radial, horizontal flow with laminar conditions (Darcy’s law valid).
• Small-slope approximation: tan(θ) ≈ slope of water table/potentiometric surface.

Concept / Approach:

Under these assumptions, continuity and Darcy’s law yield logarithmic or algebraic relations linking discharge to head at two radii. Without them, vertical components and anisotropy would require more complex models or numerical methods.

Step-by-Step Solution:

Verification / Alternative check:

Field data often deviate due to partial penetration, boundaries, or heterogeneity, but the assumptions are the textbook foundation for the derivation.

Why Other Options Are Wrong:

• Each single assumption is necessary; the comprehensive set (all the above) is the correct choice.

Common Pitfalls:

• Applying Thiem’s formula when partial penetration or leakage is significant.
• Using high pumping rates that violate laminar flow assumptions near the well.

Final Answer:

All the above.