assumptions are one of the main approaches to simplifying the unconfined flow problem and making it analytically tractable. In the unconfined flow problem both the head and the location of the water table are unknowns; the Dupuit assumptions eliminate one of the unknowns.

Historical Developments after Dupuit
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@narasimhan98 and @vries2007 give detailed historical accounts of groundwater hydrology and soil mechanics; only history relevant to well test analysis is given here. @forchheimer1886 first recognized the Laplace equation $\nabla^2 h = 0$ governed two-dimensional steady confined groundwater flow (to which is a solution), allowing analogies to be drawn between groundwater flow and steady-state heat conduction, including the first application of conformal mapping to solve a groundwater flow problem. @slichter1898 also arrived at the Laplace equation for groundwater flow, and was the first to account for a vertical flow component. Utilizing Dupuit’s assumptions, @forchheimer1898 developed the steady-state unconfined differential equation (to which is a solution), $\nabla^2 h^2=0$. @boussinesq1904 first gave the transient version of the confined groundwater flow equation $\alpha_s \nabla^2 h = \partial h/\partial t$ (where $\alpha_s=K/S_s$ is hydraulic diffusivity \[L$^2$/T\] and $S_s$ is specific storage \[1/L\]), based upon analogy with transient heat conduction.

In Prague, @thiem1906 was possibly the first 