Lizeth Paola Barrero RiañoPetroleum EnginneringIndustrial University of

Santander2010

A mathematical model can be A mathematical model can be defined broadly, as a formulation defined broadly, as a formulation or an equation that expresses the or an equation that expresses the

essential characteristics of a essential characteristics of a physical system or process in physical system or process in

mathematical terms. Its variables mathematical terms. Its variables are obtained by studying the are obtained by studying the

physical laws that are involved in physical laws that are involved in the process.the process.

Overall, the model can be represented by the functional relationship of the form:

Dependent = f (independent variables, parameters, force Dependent = f (independent variables, parameters, force functions )functions )variablesvariables

Darcy's Law is a generalized relationship for flow in porous media. It shows the volumetric flow rate is a function of the flow area, elevation, fluid pressure and a proportionality constant. It may be stated in several different forms depending on the flow conditions..

Where:

Q = Volumetric flow rate (m3/s or ft3/s),A = Flow area perpendicular to L (m2 or ft2),K = Hydraulic conductivity (m/s or ft/s),l = Flow path length (m or ft),h = Hydraulic head (m or ft), andD = Denotes the change in h over the path L.

The hydraulic head at a specific point, h is the sum of the pressure head and the elevation, or

Where:

p = water pressure (N/m2, lb/ft2),r = water density (kg/m3),g = water specific weight (lb/ft3),g = acceleration of gravity (m/s2 or ft/s2), andz = elevation (m or ft).

h = (p/r g + z) Normal SI form of the equation__ h = (p/g + z)Usual form used with English units

CHAPRA, Steven. Métodos números para ingenieros. Third edition. McGraw-Hill Editorial. 2000

Article: Conceptos básicos de modelación matemática y simulación computacional de sistemas biológicos una herramienta útil para la docencia y la investigación. Authors: Alejandro Pelaez and Sergio Mejia. CES Odontología Magazine Vol. 3 No 1.2000

http://bioen.okstate.edu/Darcy/LaLoi/basics.htm