Peer-Reviewed Article December 5, 2007
A generalised groundwater flow equation using the concept of non-integer order derivatives
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Published in: Water S.A.
Publisher: Water Research Commission • South Africa • 0378-4738 • 1816-7950
Abstract
The classical Darcy law is generalised by regarding the water flow as a function of a non-integer order derivative of the piezometric head. This generalised law and the law of conservation of mass are then used to derive a new equation for groundwater flow. Numerical solutions of this equation for various fractional orders of the derivatives are compared with experimental data and the Barker generalised radial flow model for which a fractal dimension for the flow is assumed. Water SA Vol.32 (1) 2005: pp.1-7