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# Numerical methods

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### Numerical methods

1. 1. Lizeth Paola Barrero Riaño Petroleum Enginnering Industrial University of Santander 2010
2. 2. <ul><li>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. </li></ul>
3. 4. Overall , the model can be represented by the functional relationship of the form: Dependent = f (independent variables, parameters, force functions ) variables
4. 5. <ul><li>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.. </li></ul>
5. 6. 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.
6. 7. The hydraulic head at a specific point, h is the sum of the pressure head and the elevation, or Where: p = water pressure (N/m 2 , lb/ft 2 ), r = water density (kg/m 3 ), g = water specific weight (lb/ft 3 ), g = acceleration of gravity (m/s 2 or ft/s 2 ), and z = elevation (m or ft). <ul><ul><li>h = (p/ r g + z) N ormal SI form of the equation __ </li></ul></ul><ul><ul><li>h = (p/ g + z) Usual form used with English units </li></ul></ul>
7. 8. 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