A general solution of the drawdown in a large diameter well discharging at a constant rate from a homogeneous, isotropic confined aquifer with nonlinear flow results from estimating the quantity of water withdrawn from storage within the well. Estimates for nonlinear flows toward large diameter wells are obtained by finite difference. Results are presented as a function of turbulence factors. The initial transients are linear and similar to Darcian flow, but with higher values. Estimates at moderate to long drawdown times permit determination of the nonlinear aquifer flow parameters (i.e., capacitance, turbulence factor and transmissivity). Results for large diameter wells merge asymptotically with those for small diameter wells. As an example, these predictions are used to analyze field data obtained for the Quaternary deposit aquifers in the western part of the Kingdom of Saudi Arabia.