Forchheimer and added mass effects in the flow towards a well

Abstract

In this note, we examine the flow towards a well in a confined aquifer in the presence of an interaction force defined by the sum of three terms, namely, a Darcy term (linear in the velocity), a Forchheimer term (quadratic in the velocity), and an added-mass term (linear in the acceleration). We obtain the exact dynamic solution for the piezometric head distribution around the well and investigate the relative importance of the non-Darcian terms.In the aforementioned equations, p is the pressure, e z is the unit vector pointing upward (associated to the vertical coordinate z: e z = grad z) and r is the water density.