1. MATHEMATICAL MODEL

2. General Purpose

3. Introduction A mathematical model is defined as a description from the point of view of mathematics of a fact or phenomenon of the real world, the size of the population to physical phenomena such as speed, acceleration or density.

4. Process to develop a mathematical model

10. Gradient Fig.2 Elkin slides santafé.2009.Metodos Numerical Engineering function given its gradient vector Gradient Scalar field

11. Divergence

12. Rotacinal

13. Laplacian Scalar field Vector field

14. Finite difference approximation GEOMETRIC DEFINITION Fig.3 Elkin slides santafé.2009.Metodos Numerical Engineering

15. progressive regressive central

16. Types of differential equations Elliptical Satellite Hyperbolic Laplace equation (Steady state two-dimensional space) Equation heat conduction (Variable time and dimension spatial) Wave equation (Variable time and dimension spatial)

17. Fundamental Flow Equation GEOMETRIC FACTOR FLUID DENSITY FLOW RATE POROSITY SOURCES AND / OR SINKS

18. Flow in porous media: Darcy's Law c c

19. In 1856, in the French city of Dijon, the engineer Henry Darcy was responsible for study of the supply network to the city. It seems that it also had to design filters sand to purify water, so I was interested in the factors influencing the flow of water through the sandy, and presented the results of his work as a appendix to his report of the distribution network. That little appendix has been the basis of all subsequent physico-mathematical studies on groundwater flow. In today's laboratories have equipment similar to that used Darcy, and are called constant head permeameter

20. Fig.4 constant head permeameter Q = Caudal Δ h = Potential Difference entre A y B Δ l = Distance between A y B Hydraulic gradient = section Basically a permeameter is a recipient of constant section which makes Flush connecting one end of a high constant level tank. In the other end is regulated by an outflow valve in each experiment also maintains the flow constant. Finally, measure the height of the water column at various points

21. Section If the environment changes but the relationship is fulfilled K constant changes. This was called permeability.

22. Conservation of Momentum caudal section x velocity Velocidad Darcy : Caudal / Saccion total This is false because the water does not circulate throughout the cross section

23. Limitations of Darcy's law The proportionality constant K is not proper or other feature the porous medium. PERMEABILITY INTRINSIC SPECIFIC WEIGHT FLUID VISCOSITY DYNAMICS FLUID

24. In some circumstances the relationship between Q and the gradient Hydraulic non-linear. This can happen when the value of K is very low or very high speeds. Darcy is met Darcy is not met can be fulfilled or not

25. Equations of State Incompressible fluid Fluid slightly compressible Compressible fluid constant

26. Bibliography http://webcache.googleusercontent.com/search?q=cache:trQqOqKXXucJ:www.monografias.com/trabajos12/moma/moma.shtml+CUAL+ES+EL+OBJETIVO+DE+UN+MODELO+MATEMATICO&cd=1&hl=es&ct=clnk&gl=co Elkin slides santafé.2009.Metodos Numerical Engineering F. Javier Sánchez San Román‐‐Dpto. Geología‐‐Univ. Salamanca (España) http://web.usal.es/javisan/hidro