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# Numerical methods

## on May 10, 2010

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## Numerical methodsPresentation Transcript

• 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.
• Characteristics
• 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