MATHEMATICALMODELS Lizeth Paola Barrero Riaño PetroleumEnginnering Industrial University of Santander 2010
Definition A mathematical model can be defined broadly, as a formulation or an equation that expresses the essential characteristics of a physical system or process in mathematical terms. Its variables are obtained by studying the physical laws that are involved in the process.
Components Overall, the model can be represented by the functional relationship of the form: Dependent = f (independent variables, parameters, forcefunctions ) variables
Darcy’s law 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..
One-Dimensional Flow 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), and D = Denotes the change in h over the path L.
Thehydraulic head at a specificpoint, histhesum of thepressure head and theelevation, or h = (p/r g + z) Normal SI form of the equation__ h = (p/g + z)Usual form used with English units Where: p = waterpressure (N/m2, lb/ft2),r = waterdensity (kg/m3),g = waterspecificweight (lb/ft3),g = acceleration of gravity (m/s2or ft/s2), andz = elevation (m or ft).
Bibliography CHAPRA, Steven. Métodos números para ingenieros. Thirdedition. 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